Pre-Calc/Trig Unit 3: Analytic Trig and Applications/7.4 Vectors Angle between vectors Find the angle between the pair of vectors to the nearest tenth of a degree.
(Include degree symbol in answer--located in "x" menu).

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨§lt;¨ close=¨§#62;¨»«mrow»«mn»5«/mn»«mo»,«/mo»«mn»5«/mn»«/mrow»«/mfenced»«mo»§#160;«/mo»«mo»,«/mo»«mo»§#160;«/mo»«mfenced open=¨§lt;¨ close=¨§#62;¨»«mrow»«mo»-«/mo»«mn»3«/mn»«mo»,«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»a«/mi»«mo»§#160;«/mo»«/mrow»«/mfenced»«/math»

]]> 1.0000000 0.3333333 0 0 #answer]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>arccos</mi><mo>(</mo><mfrac><mrow><mo>(</mo><mo>-</mo><mn>15</mn><mo>+</mo><mn>5</mn><mo>*</mo><mi>a</mi><mo>)</mo></mrow><mrow><mn>5</mn><mo>*</mo><msqrt><mn>2</mn></msqrt><mo>*</mo><msqrt><mrow><mn>9</mn><mo>+</mo><msup><mi>a</mi><mn>2</mn></msup></mrow></msqrt></mrow></mfrac><mo>)</mo><mo>*</mo><mn>1</mn><mo>.</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mo>=</mo><mi>convert</mi><mo>(</mo><mi>t</mi><mo>,</mo><csymbol definitionURL="http://.../units/degree/angular">°</csymbol><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>answer</mi><mo>=</mo><mi>w</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>a</mi><mi>ns</mi><mi>w</mi><mi mathvariant="normal">e</mi><mi>r</mi></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m, y, z, a, f, p, n, µ, d, da, h, G, T, P, E, Z, Y</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-1)</option><option name="relative_tolerance">false</option><option name="precision">3</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession">null</data></localData></question> Find component form of vector Find the component form of the indicated vector.
Let u = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨§lt;¨ close=¨§#62;¨»«mrow»«mo»-«/mo»«mn»9«/mn»«mo»,«/mo»«mo»-«/mo»«mn»9«/mn»«/mrow»«/mfenced»«/math», v =«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨§lt;¨ close=¨§#62;¨»«mrow»«mo»#«/mo»«mi»a«/mi»«mo»§#160;«/mo»«mo»,«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»b«/mi»«mo»§#160;«/mo»«/mrow»«/mfenced»«/math». Find -u + 9v.

]]> 1.0000000 0.3333333 0 true true abc #t1

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]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mfenced close="]" open="["><mrow><mn>9</mn><mo>+</mo><mn>9</mn><mo>*</mo><mi>a</mi><mo>,</mo><mn>9</mn><mo>+</mo><mn>9</mn><mo>*</mo><mi>b</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mfenced close="]" open="["><mrow><mn>9</mn><mo>-</mo><mn>9</mn><mo>*</mo><mi>a</mi><mo>,</mo><mn>9</mn><mo>-</mo><mn>9</mn><mo>*</mo><mi>b</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t3</mi><mo>=</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>9</mn><mo>+</mo><mn>9</mn><mo>*</mo><mi>a</mi><mo>,</mo><mo>-</mo><mn>9</mn><mo>+</mo><mn>9</mn><mo>*</mo><mi>b</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t4</mi><mo>=</mo><mfenced close="]" open="["><mrow><mn>9</mn><mo>*</mo><mn>9</mn><mo>*</mo><mi>a</mi><mo>,</mo><mn>9</mn><mo>*</mo><mn>9</mn><mo>*</mo><mi>b</mi></mrow></mfenced></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession">null</data></localData></question> Find dot product Find the dot product between these vectors

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨§lt;¨ close=¨§#62;¨»«mrow»«mo»#«/mo»«mi»a«/mi»«mo»§#160;«/mo»«mo»,«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»b«/mi»«mo»§#160;«/mo»«/mrow»«/mfenced»«mo»§#160;«/mo»«mo»§#160;«/mo»«mfenced open=¨§lt;¨ close=¨§#62;¨»«mrow»«mo»#«/mo»«mi»c«/mi»«mo»§#160;«/mo»«mo»,«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»d«/mi»«mo»§#160;«/mo»«/mrow»«/mfenced»«/math»

]]> 1.0000000 0.3333333 0 0 #answer]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>answer</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>c</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>d</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>a</mi><mi>n</mi><mi>s</mi><mi>w</mi><mi mathvariant="normal">e</mi><mi>r</mi></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession">null</data></localData></question> Find dot product (i/j format) Find the dot product between these vectors

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»a«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨»i«/mi»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»b«/mi»«mo»§#160;«/mo»«mi mathvariant=¨bold-italic¨»j«/mi»«mspace linebreak=¨newline¨/»«mo»#«/mo»«mi»c«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨»i«/mi»«mo»§#160;«/mo»«mo»+«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»d«/mi»«mo»§#160;«/mo»«mi mathvariant=¨bold-italic¨»j«/mi»«/math»

]]> 1.0000000 0.3333333 0 0 #answer]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>answer</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>c</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>d</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>a</mi><mi>n</mi><mi>s</mi><mi>w</mi><mi mathvariant="normal">e</mi><mi>r</mi></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession">null</data></localData></question> Find magnitude and direction angle Find the magnitude and direction angle (to the nearest unit) for each vector. Give the measure of the direction angle as an angle in [0,360°]. Also round to the nearest unit. Include degree symbol in answer for angle.

]]> 1.0000000 0.3333333 0 0 magnitude=#mdirection angle=#d]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>16</mn><mo>,</mo><mo>-</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>16</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><msqrt><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup></mrow></msqrt><mo>*</mo><mn>1</mn><mo>.</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>convert</mi><mo>(</mo><mi>atan</mi><mo>(</mo><mfrac><mi>b</mi><mfenced close="|" open="|"><mi>a</mi></mfenced></mfrac><mo>)</mo><mo>,</mo><csymbol definitionURL="http://.../units/degree/angular">°</csymbol><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mn>180</mn><csymbol definitionURL="http://.../units/degree/angular">°</csymbol><mo>-</mo><mi>t</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>convert</mi><mo>(</mo><mi>atan</mi><mo>(</mo><mfrac><mi>b</mi><mfenced close="|" open="|"><mi>a</mi></mfenced></mfrac><mo>)</mo><mo>,</mo><csymbol definitionURL="http://.../units/degree/angular">°</csymbol><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>45.</mn><mo> </mo><csymbol definitionURL="http://.../units/degree/angular">°</csymbol></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mn>180</mn><csymbol definitionURL="http://.../units/degree/angular">°</csymbol><mo>-</mo><mi>t</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>135.</mn><mo> </mo><csymbol definitionURL="http://.../units/degree/angular">°</csymbol></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">m</mi><mi>ag</mi><mi>n</mi><mi mathvariant="normal">i</mi><mi>t</mi><mi>u</mi><mi>d</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo>#</mo><mi mathvariant="normal">m</mi><mspace linebreak="newline"/><mi>dir</mi><mi mathvariant="normal">e</mi><mi>c</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi>o</mi><mi>n</mi><mo> </mo><mi>a</mi><mi>ng</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo>#</mo><mi>d</mi></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m, y, z, a, f, p, n, µ, d, da, h, G, T, P, E, Z, Y</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-0)</option><option name="relative_tolerance">false</option><option name="precision">3</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">50 50</data><data name="inputField">popupEditor</data><data name="casSession">null</data></localData></question> Find scalar multiple Find the indicated vector.
Let a = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced open=¨§lt;¨ close=¨§#62;¨»«mrow»«mo»#«/mo»«mi»a«/mi»«mo»§#160;«/mo»«mo»,«/mo»«mo»§#160;«/mo»«mo»#«/mo»«mi»b«/mi»«mo»§#160;«/mo»«/mrow»«/mfenced»«/math». Find -3a.

]]> 1.0000000 0.3333333 0 true true ABCD #t1

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]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>3</mn><mo>*</mo><mi>a</mi><mo>,</mo><mo>-</mo><mn>3</mn><mo>*</mo><mi>b</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mfenced close="]" open="["><mrow><mn>3</mn><mo>*</mo><mi>a</mi><mo>,</mo><mn>3</mn><mo>*</mo><mi>b</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t3</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>a</mi><mo>+</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>*</mo><mi>b</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t4</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>a</mi><mo>-</mo><mn>3</mn><mo>,</mo><mi>b</mi><mo>-</mo><mn>3</mn></mrow></mfenced></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession">null</data></localData></question> Find the angle between the pair of vectors to the nearest tenth of a degree., Find the angle between the pair of vectors to the nearest tenth of a degree.

]]> 1.0000000 0.3333333 0 0 #answer]]> Great job!!

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>88</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>210</mn><mo>,</mo><mn>350</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>answer</mi><mo>=</mo><mi>b</mi><mo>*</mo><mo>(</mo><mi>sin</mi><mo>(</mo><mi>a</mi><csymbol definitionURL="http://.../units/degree/angular">°</csymbol><mo>)</mo><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>a</mi><mi>ns</mi><mi>w</mi><mi mathvariant="normal">e</mi><mi>r</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m, y, z, a, f, p, n, µ, d, da, h, G, T, P, E, Z, Y</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-1)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession">null</data></localData></question> Did you draw a vector and its components on a graph?

]]> Did you use the appropriate trig function for opposite and hypotenuse in a right triangle?

]]> Two forces act at a point in the plane. The angle between the two forces is ... Two forces act at a point in the plane. The angle between the two forces is given. Find the magnitude of the resultant force.

forces of 25.0 and 31.8 lb, forming an angle of 162.8°

]]> 1.0000000 0.3333333 0 0 11 *

]]> Write the vector in the form <a, b>.

]]> 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 1.0000000 0.3333333 0 true true abc ]]> 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 Incorrect ]]> /9j/4AAQSkZJRgABAQAAAQABAAD/2wBDAAMCAgMCAgMDAwMEAwMEBQgFBQQEBQoHBwYIDAoMDAsKCwsNDhIQDQ4RDgsLEBYQERMUFRUVDA8XGBYUGBIUFRT/2wBDAQMEBAUEBQkFBQkUDQsNFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBQUFBT/wAARCAARAEUDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEAAwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSExBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElKU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3uLm6wsPExcbHyMnK0tPU1dbX2Nna4uPk5ebn6Onq8vP09fb3+Pn6/9oADAMBAAIRAxEAPwD9CPhFq19471XxR46e9uD4e1WaPT/D1n5rfZ30+1aVRfKmSha6mluJEmjYrLarYNgENS/ETxN4yuPGWm+EvA9xommajLptxqtzqev2M17CiJJHHHCsMU8LFnaRiX34QR/dYsMc34H+D/h7UvDl38MvHPgnTPE2g+DrtU8NSa9pMd5ayaU6E2YjMiOoktk8yyYF2mYWqTSYFymdHWPgRN4e1DRr/wCFN/oXw3l0+zuNObTx4fW50yS3mkWVittDNb7JVkQMHDEfM4ZG3AhWu1fb/gO3/k1u+n3De2m+n5q/4X+Zf8LeMfF/xT+C3h7xD4cbQ/DviXU4oZJ/7Ugl1CztiH2zhUjkhaTG1gvzp2z0xXFW/iL4zyaHq+uz+OPh7b+HbCSdY9RHgy+d7xY9q5jhGrcAyCVVO8l9qELhga7aD4V+INF+Hp8GeH/FsOjaZFpVvp1rfrprPqMMgbFxcGUThC8iE7MRr5bnf84wlbGr/DaO/n8GWVpeLp3hXw7Isx0SKAkXTwootFMm/wCWOFh5m3adzpEcjYQ02ld6/wBeX6Lr1sJWt/X9a7Pt0ubHgZ/EMnhDSH8WCxHiRrdWv102Jo7dZTyQitJIQB0++3IPJFeRab8XvHUuueF9euo/D58C+IvEE+gwaYltMmpWqq06QXTXJmMcm9rfJhEKFRKB5jFDu9c0qfxBc+KdZ+2wWtr4ehSGKwXZm5mlwWllZxIV8r5kVVKq+UkJ4K15t4f+BGu6LrmmQT+MbbUPBmi6pdazpGkSaQwvIriXzSqz3f2jbLFE1xKURYY24jDO207qd3JNW79e609Wr2vs92hW91ryf320fonv38xfi58ftO8HeMbbwXb+KvCvhDWZbaO7m1jxfcKtpbrIzrDFHD50LXE0jRP+7WVNiqXJPyI+P+0r428YwP4Q8I+B5rK317VNYgik1S4uJYIIbmKCe9tYHERL+TNLZKk6gk/Z3kUcyqy2/E37P3iTxDrWqaunivw/a3/ibQovD/ih38LeeLqBPNG6zD3RNuSs8o2zG5TIQlDtIbhP2gP2ZdRtJNG8ZeBtW1V77w3cwajb+GpL3Wrr+2L9IfstvCpi1GOCzRw6I83kbY13PI3lCVTrScVJc+2v9bbenzW7ddG/J/fbT8futvrp9HeAPGtj8RfBuk+I9PiuLW3v4RI1neqqXNnKCVltrhFZhHPDIrxSR5JSSN1PKmiqnwt8C/8ACt/AmmaFJff2rfx+bdajqfleT9vv55XnvLrytzCLzriWaXy1O1N+1cKoAKzEdXRRRQAUUUUAFFFFABRRRQAUUUUAf//Z Incorrect ]]> 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Incorrect ]]> 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Correct