What is the projection of $< 5, 0, - 2 >$ $<5,0,-2 >$ onto $< 1, - 1, 0 >$ $<1,-1,0 >$ ?

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What is the projection of $< 5, 0, - 2 >$ $<5,0,-2 >$ onto $< 1, - 1, 0 >$ $<1,-1,0 >$ ?

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Answer 1 · 2016-02-14T19:01:14

$\to c = < \frac{5}{2}, - \frac{5}{2}, 0 >$ $vec c=<5/2,-5/2,0>$

Explanation:

$\to a = < 5, 0, - 2 >$ $vec a=<5,0,-2>$
$\to b = < 1, - 1, 0 >$ $vec b=<1,-1,0>$
$\to a \cdot \to b = 5 \cdot 1 + 0 \cdot (- 1) + 0 \cdot (- 2) = 5$ $vec a*vec b=5*1+0*(-1)+0*(-2)=5$
$dot product between vec a and vec b;$ $"dot product between vec a and vec b;"$
$| b | = \sqrt{1^{2} + 1^{2} + 0^{2}} = \sqrt{2}$ $|b|=sqrt(1^2+1^2+0^2)=sqrt 2$
$\to c = \frac{\to a \cdot \to b}{| b | \cdot | b |} \cdot \to b$ $vec c=(vec a*vec b)/(|b|*|b|)*vec b$
$\to c = \frac{5}{\sqrt{2} \cdot \sqrt{2}} \cdot < 1, - 1, 0 >$ $vec c=5/(sqrt 2*sqrt 2)*<1,-1,0>$
$\to c = \frac{5}{2} < 1, - 1, 0 >$ $vec c=5/2<1,-1,0>$
$\to c = < \frac{5}{2}, - \frac{5}{2}, 0 >$ $vec c=<5/2,-5/2,0>$

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What is the projection of $< 5, 0, - 2 >$ $<5,0,-2 >$ onto $< 1, - 1, 0 >$ $<1,-1,0 >$ ?

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Explanation:

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