What is the projection of $< 0, 2, - 2 >$ $< 0 , 2, -2 >$ onto $< 3, - 6, 7 >$ $< 3 , -6, 7 >$ ?

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What is the projection of $< 0, 2, - 2 >$ $< 0 , 2, -2 >$ onto $< 3, - 6, 7 >$ $< 3 , -6, 7 >$ ?

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Answer 1 · 2017-01-01T17:33:11

$P r o j_{\to v} \to u = \frac{- 26}{94} < 3, - 6, 7 >$ $Proj_vec v vec u= (-26)/94 <3,-6,7>$ = $< \frac{- 78}{94}, \frac{156}{94}, \frac{- 182}{94} >$ $< (-78)/94, 156/94, (-182)/94 >$

Explanation:

Let $\to u$ $vec u$ be <0,2,-2> and $\to v$ $vec v$ be <3,-6,7>. The projection of $\to u$ $vec u$ on $\to v$ $vec v$ is represented as

$P r o j_{\to v} \to u$ $Proj_vec v vec u$ = $\frac{\to u . \to v}{{∣ ∣ ∣ ∣ \to v ∣ ∣ ∣ ∣}^{2}} \to v$ $(vec u .vec v) /||vec v||^2 vec v$

In the present case $\to u . \to v$ $vec u .vec v$ = 0(3) +2(-6) +(-2)(7) = -26

Also ${| | v | |}^{2}$ $||v||^2$ = $3^{2} + {(- 6)}^{2} + 7^{2}$ $3^2 +(-6)^2 + 7^2$ = 94

Thus $P r o j_{\to v} \to u = \frac{- 26}{94} < 3, - 6, 7 >$ $Proj_vec v vec u= (-26)/94 <3,-6,7>$ = $< \frac{- 78}{94}, \frac{156}{94}, \frac{- 182}{94} >$ $< (-78)/94, 156/94, (-182)/94 >$

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What is the projection of $< 0, 2, - 2 >$ $< 0 , 2, -2 >$ onto $< 3, - 6, 7 >$ $< 3 , -6, 7 >$ ?

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Explanation:

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What is the projection of <0,2,−2>< 0 , 2, -2 > onto <3,−6,7>< 3 , -6, 7 >?

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Explanation:

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What is the projection of $< 0, 2, - 2 >$ $< 0 , 2, -2 >$ onto $< 3, - 6, 7 >$ $< 3 , -6, 7 >$ ?