What is the projection of $< - 2, 3, 7 >$ $<-2,3,7 >$ onto $< 1, 6, 1 >$ $<1,6,1 >$ ?

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What is the projection of $< - 2, 3, 7 >$ $<-2,3,7 >$ onto $< 1, 6, 1 >$ $<1,6,1 >$ ?

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Answer 1 · 2016-02-15T21:51:02

$p r o j_{\to B} \to A = < \frac{23}{38}, \frac{138}{38}, \frac{23}{38} >$ $proj_vec B vec A = <23/38,138/38,23/38>$

Explanation:

$\to A = < - 2, 3, 7 >$ $vec A= <-2,3,7 >$
$\to B = < 1, 6, 1 >$ $vec B= <1,6,1 >$
$p r o j_{\to B} \to A = \frac{\to A \cdot \to B}{{∣ ∣ ∣ ∣ ∣ ∣ \to B ∣ ∣ ∣ ∣ ∣ ∣}^{2}} \cdot \to B$ $proj_vec B vec A =(vec A * vec B)/|| vec B||^2 * vec B$
$\to A \cdot \to B = - 2 \cdot 1 + 3 \cdot 6, 7 \cdot 1$ $vec A * vec B= -2*1 +3*6 ,7*1$
$\to A \cdot \to B = - 2 + 18 + 7 = 23$ $vec A * vec B= -2+18+7=23$
${∣ ∣ ∣ ∣ ∣ ∣ \to B ∣ ∣ ∣ ∣ ∣ ∣}^{2} = 1^{2} + 6^{2} + 1^{2} = 38$ $|| vec B||^2=1^2+6^2+1^2=38$
$p r o j_{\to B} \to A = \frac{23}{38} \cdot < 1, 6, 1 >$ $proj_vec B vec A =23/38 * <1,6,1 >$
$p r o j_{\to B} \to A = < \frac{23}{38}, \frac{138}{38}, \frac{23}{38} >$ $proj_vec B vec A = <23/38,138/38,23/38>$

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What is the projection of $< - 2, 3, 7 >$ $<-2,3,7 >$ onto $< 1, 6, 1 >$ $<1,6,1 >$ ?

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Explanation:

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What is the projection of <-2,3,7 ><−2,3,7><-2,3,7 > onto <1,6,1 ><1,6,1><1,6,1 >?

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