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Let three vectors 
be such that 
 is coplanar with 
 is perpendicular to 
 then the value of 2 
 is____________.
Let three vectors be such that is coplanar with is perpendicular to then the value of 2 is____________.
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1 Answer
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From Solving <p><!-- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1819009496"> </o:OLEObject></xml><![endif]--> <span contenteditable="false"> <math> <mrow> <mover accent="true"> <mi>c</mi> <mo>→</mo> </mover> <mo>=</mo> <mi>α</mi> <mover accent="true"> <mi>a</mi> <mo>→</mo> </mover> <mo>+</mo> <mi>β</mi> <mover accent="true"> <mi>b</mi> <mo>→</mo> </mover> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mrow> <mo>(</mo> <mrow> <mi>i</mi> </mrow> <mo>)</mo> </mrow> </mrow> </math> </span></p><p>  <span contenteditable="false"> <math> <mrow> <mover accent="true"> <mi>a</mi> <mo>→</mo> </mover> <mo>.</mo> <mover accent="true"> <mi>c</mi> <mo>→</mo> </mover> <mo>=</mo> <mn>7</mn> <mtext> </mtext> <mtext> </mtext> <mtext> </mtext> <mtext> </mtext> <mtext> </mtext> <mtext> </mtext> <mover accent="true"> <mi>b</mi> <mo>→</mo> </mover> <mo>.</mo> <mover accent="true"> <mi>c</mi> <mo>→</mo> </mover> <mo>=</mo> <mn>0</mn> </mrow> </math> </span>         <!-- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1026" DrawAspect="Content" ObjectID="_1819009497"> </o:OLEObject></xml><![endif]--></p><p><span contenteditable="false"> <math> <mrow> <mover accent="true"> <mi>a</mi> <mo>→</mo> </mover> <mo>=</mo> <mo>−</mo> <mover accent="true"> <mi>i</mi> <mo>^</mo> </mover> <mo>+</mo> <mover accent="true"> <mi>j</mi> <mo>^</mo> </mover> <mo>+</mo> <mover accent="true"> <mi>k</mi> <mo>^</mo> </mover> <mo>⇒</mo> <mrow> <mo>|</mo> <mrow> <mover accent="true"> <mi>a</mi> <mo>→</mo> </mover> </mrow> <mo>|</mo> </mrow> <mo>=</mo> <mroot> <mrow> <mn>3</mn> </mrow> <mrow></mrow> </mroot> </mrow> </math> </span>           <!-- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1027" DrawAspect="Content" ObjectID="_1819009498"> </o:OLEObject></xml><![endif]--></p><p><span contenteditable="false"> <math> <mrow> <mover accent="true"> <mi>b</mi> <mo>→</mo> </mover> <mo>=</mo> <mn>2</mn> <mover accent="true"> <mi>i</mi> <mo>^</mo> </mover> <mo>+</mo> <mover accent="true"> <mi>k</mi> <mo>^</mo> </mover> <mo>⇒</mo> <mrow> <mo>|</mo> <mrow> <mover accent="true"> <mi>b</mi> <mo>→</mo> </mover> </mrow> <mo>|</mo> </mrow> <mo>=</mo> <mroot> <mrow> <mn>5</mn> </mrow> <mrow></mrow> </mroot> <mtext> </mtext> <mover accent="true"> <mi>a</mi> <mo>→</mo> </mover> <mo>.</mo> <mover accent="true"> <mi>b</mi> <mo>→</mo> </mover> <mo>=</mo> <mo>−</mo> <mn>2</mn> <mo>+</mo> <mn>1</mn> <mo>=</mo> <mo>−</mo> <mn>1</mn> </mrow> </math> </span>           <!-- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1028" DrawAspect="Content" ObjectID="_1819009499"> </o:OLEObject></xml><![endif]--></p><p>From <!-- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1029" DrawAspect="Content" ObjectID="_1819009500"> </o:OLEObject></xml><![endif]--> <span contenteditable="false"> <math> <mrow> <mrow> <mo>(</mo> <mrow> <mi>i</mi> </mrow> <mo>)</mo> </mrow> <mover accent="true"> <mi>a</mi> <mo>→</mo> </mover> <mo>.</mo> <mover accent="true"> <mi>c</mi> <mo>→</mo> </mover> <mo>=</mo> <mi>α</mi> <msup> <mrow> <mrow> <mo>|</mo> <mrow> <mover accent="true"> <mi>a</mi> <mo>→</mo> </mover> </mrow> <mo>|</mo> </mrow> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mi>β</mi> </mrow> </math> </span></p><p><span contenteditable="false"> <math> <mrow> <mn>3</mn> <mi>α</mi> <mo>−</mo> <mi>β</mi> <mo>=</mo> <mn>7</mn> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mrow> <mo>(</mo> <mrow> <mi>i</mi> <mi>i</mi> </mrow> <mo>)</mo> </mrow> </mrow> </math> </span>           <!-- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1030" DrawAspect="Content" ObjectID="_1819009501"> </o:OLEObject></xml><![endif]--></p><p><span contenteditable="false"> <math> <mrow> <mover accent="true"> <mi>b</mi> <mo>¯</mo> </mover> <mo>.</mo> <mover accent="true"> <mi>c</mi> <mo>¯</mo> </mover> <mo>=</mo> <mi>α</mi> <mover accent="true"> <mi>b</mi> <mo>¯</mo> </mover> <mo>.</mo> <mover accent="true"> <mi>a</mi> <mo>¯</mo> </mover> <mo>+</mo> <mi>β</mi> <msup> <mrow> <mrow> <mo>|</mo> <mrow> <mover accent="true"> <mi>b</mi> <mo>→</mo> </mover> </mrow> <mo>|</mo> </mrow> </mrow> <mrow> <mn>2</mn> </mrow> </msup> <mo>⇒</mo> <mo>−</mo> <mi>α</mi> <mo>+</mo> <mn>5</mn> <mi>β</mi> <mo>=</mo> <mn>0</mn> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mrow> <mo>(</mo> <mrow> <mi>i</mi> <mi>i</mi> <mi>i</mi> </mrow> <mo>)</mo> </mrow> </mrow> </math> </span>           <!-- [if gte mso 9]><xml> <o:OLEObject Type="Embed" ProgID="Equation.DSMT4" ShapeID="_x0000_i1031" DrawAspect="Content" ObjectID="_1819009502"> </o:OLEObject></xml><![endif]--></p><p>Solving<span contenteditable="false"> <math> <mrow> <mi>α</mi> <mo>=</mo> <mfrac> <mrow> <mn>5</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> <mtext> </mtext> <mtext> </mtext> <mtext> </mtext> <mi>a</mi> <mi>n</mi> <mi>d</mi> <mtext> </mtext> <mtext> </mtext> <mtext> </mtext> <mi>β</mi> <mo>=</mo> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> </mrow> </math> </span></p><p><span contenteditable="false"> <math><mrow><mo>⇒</mo><mn>2</mn><msup><mrow><mrow><mo>|</mo><mrow><mover accent="true"><mi>a</mi><mo>→</mo></mover><mo>+</mo><mover accent="true"><mi>b</mi><mo>→</mo></mover><mo>+</mo><mover accent="true"><mi>c</mi><mo>→</mo></mover></mrow><mo>|</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mn>7</mn><mn>5</mn></mrow></math> </span>           </p><p> </p> 
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