1MA 04. VECTORS/1MA.04.3 Bases 1MA.04.3.12Q VectorsDependents?4 exercicis Calcula u₁v₂ - u₂v₁ i esbrina si els parells següents de vectors són Independents o Dependents (escriu I o D, AMB MAJÚSCULES):

Vectors

a) (#a1, #a2) i (#a3, #a4)

b) (#b1, #b2) i (#b3, #b4)

c) (#c1, #c2) i (#c3, #c4)

d) (#d1, #d2) i (#d3, #d4)

]]> Els vectors són:

a) #G1

b) #G2

c) #G3

d) #G4

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definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>t4</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>d1</mi><mo>=</mo><mi>d11</mi></mtd></mtr><mtr><mtd><mi>d2</mi><mo>=</mo><mi>d12</mi></mtd></mtr><mtr><mtd><mi>d3</mi><mo>=</mo><mi>d13</mi></mtd></mtr><mtr><mtd><mi>d4</mi><mo>=</mo><mi>d14</mi></mtd></mtr><mtr><mtd><mi>s4</mi><mo>=</mo><mi>d11</mi><mo>*</mo><mi>d14</mi><mo>-</mo><mi>d12</mi><mo>*</mo><mi>d13</mi></mtd></mtr><mtr><mtd><mi>r4</mi><mo>=</mo><mi>I</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>d1</mi><mo>=</mo><mi>d21</mi></mtd></mtr><mtr><mtd><mi>d2</mi><mo>=</mo><mi>d22</mi></mtd></mtr><mtr><mtd><mi>d3</mi><mo>=</mo><mi>d23</mi></mtd></mtr><mtr><mtd><mi>d4</mi><mo>=</mo><mi>d24</mi></mtd></mtr><mtr><mtd><mi>s4</mi><mo>=</mo><mi>d21</mi><mo>*</mo><mi>d24</mi><mo>-</mo><mi>d22</mi><mo>*</mo><mi>d23</mi></mtd></mtr><mtr><mtd><mi>r4</mi><mo>=</mo><mi>D</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tauler</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>mostrar_eixos</mi><mo>=</mo><mi>fals</mi><mo>,</mo><mi>amplada_finestra</mi><mo>=</mo><mn>200</mn><mo>,</mo><mi>altura_finestra</mi><mo>=</mo><mn>200</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v11</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>a1</mi><mo>,</mo><mi>a2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v12</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>a3</mi><mo>,</mo><mi>a4</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>v11</mi><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>v12</mi><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mi>mida_punt</mi><mo>=</mo><mn>8</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T2</mi><mo>=</mo><mi>tauler</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>mostrar_eixos</mi><mo>=</mo><mi>fals</mi><mo>,</mo><mi>amplada_finestra</mi><mo>=</mo><mn>200</mn><mo>,</mo><mi>altura_finestra</mi><mo>=</mo><mn>200</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v21</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>b1</mi><mo>,</mo><mi>b2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v22</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>b3</mi><mo>,</mo><mi>b4</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G2</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T2</mi><mo>,</mo><mi>v21</mi><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G2</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T2</mi><mo>,</mo><mi>v22</mi><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G2</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T2</mi><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mi>mida_punt</mi><mo>=</mo><mn>8</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T3</mi><mo>=</mo><mi>tauler</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>mostrar_eixos</mi><mo>=</mo><mi>fals</mi><mo>,</mo><mi>amplada_finestra</mi><mo>=</mo><mn>200</mn><mo>,</mo><mi>altura_finestra</mi><mo>=</mo><mn>200</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v31</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>c1</mi><mo>,</mo><mi>c2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v32</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>c3</mi><mo>,</mo><mi>c4</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G3</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T3</mi><mo>,</mo><mi>v31</mi><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G3</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T3</mi><mo>,</mo><mi>v32</mi><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G3</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T3</mi><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mi>mida_punt</mi><mo>=</mo><mn>8</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T4</mi><mo>=</mo><mi>tauler</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>mostrar_eixos</mi><mo>=</mo><mi>fals</mi><mo>,</mo><mi>amplada_finestra</mi><mo>=</mo><mn>200</mn><mo>,</mo><mi>altura_finestra</mi><mo>=</mo><mn>200</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v41</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>d1</mi><mo>,</mo><mi>d2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v42</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>d3</mi><mo>,</mo><mi>d4</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G4</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T4</mi><mo>,</mo><mi>v41</mi><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G4</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T4</mi><mo>,</mo><mi>v42</mi><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G4</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T4</mi><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mi>mida_punt</mi><mo>=</mo><mn>8</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>,</mo><mi>a3</mi><mo>,</mo><mi>a4</mi><mo>,</mo><mi>s1</mi><mo>,</mo><mi>r1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>0</mn><mo>,</mo><mi>D</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>,</mo><mi>b2</mi><mo>,</mo><mi>b3</mi><mo>,</mo><mi>b4</mi><mo>,</mo><mi>s2</mi><mo>,</mo><mi>r2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>8</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>0</mn><mo>,</mo><mi>D</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>,</mo><mi>c2</mi><mo>,</mo><mi>c3</mi><mo>,</mo><mi>c4</mi><mo>,</mo><mi>s3</mi><mo>,</mo><mi>r3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>0</mn><mo>,</mo><mi>D</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>,</mo><mi>d2</mi><mo>,</mo><mi>d3</mi><mo>,</mo><mi>d4</mi><mo>,</mo><mi>s4</mi><mo>,</mo><mi>r4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>,</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>8</mn><mo>,</mo><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>24</mn><mo>,</mo><mi>I</mi></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>a</mi><mo>.</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>r</mi><mn>1</mn><mspace linebreak="newline"/><mi>b</mi><mo>.</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>r</mi><mn>2</mn><mspace linebreak="newline"/><mi>c</mi><mo>.</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>r</mi><mn>3</mn><mo> </mo><mspace linebreak="newline"/><mi mathvariant="normal">d</mi><mo>.</mo><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>r</mi><mn>4</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> u₁v₂ - u₂v₁ és igual a:

a) #s1

b) #s2

c) #s3

d) #s4

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