What is the projection of $< - 3, 7, 7 >$ $< -3, 7, 7>$ onto $< - 3, 4, - 5 >$ $< -3 , 4, -5>$ ?

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What is the projection of $< - 3, 7, 7 >$ $< -3, 7, 7>$ onto $< - 3, 4, - 5 >$ $< -3 , 4, -5>$ ?

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Answer 1 · 2017-10-19T12:04:10

The projection is $= \frac{1}{25} < - 3, 4, - 5 >$ $=1/25<-3,4,-5>$

Explanation:

The vectors are

$\to a = < - 3, 7, 7 >$ $veca=<-3,7,7>$

$\to b = < - 3, 4, - 5 >$ $vecb=<-3,4,-5>$

The projection of $\to a$ $veca$ onto $\to b$ $vecb$ is

$p r o j_{\to b} \to a = \frac{\to a . \to b}{{∣ ∣ ∣ ∣ ∣ ∣ \to b ∣ ∣ ∣ ∣ ∣ ∣}^{2}} \to b$ $proj_(vecb)veca=(veca.vecb)/(||vecb||^2)vecb$

$= \frac{< - 3, 7, 7 > . < - 3, 4, - 5 >}{{| | < - 3, 4, - 5 > | |}^{2}} < - 3, 4, - 5 >$ $=(<-3,7,7>.<-3,4,-5>)/(||<-3,4,-5>||^2)<-3,4,-5>$

$= \frac{{(- 3)}^{2} + (7.4) + (7 . - 5)}{{(- 3)}^{2} + (4.4) + (- 5 . - 5)} < - 3, 4, - 5 >$ $=((-3)^2+(7.4)+(7.-5))/((-3)^2+(4.4)+(-5.-5))<-3,4,-5>$

$= (\frac{2}{50}) < - 3, 4, - 5 >$ $=(2/50)<-3,4,-5>$

$= \frac{1}{25} < - 3, 4, - 5 >$ $=1/25<-3,4,-5>$

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What is the projection of $< - 3, 7, 7 >$ $< -3, 7, 7>$ onto $< - 3, 4, - 5 >$ $< -3 , 4, -5>$ ?

1 Answer

Explanation:

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What is the projection of <−3,7,7>< -3, 7, 7> onto <−3,4,−5>< -3 , 4, -5>?

1 Answer

Explanation:

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What is the projection of $< - 3, 7, 7 >$ $< -3, 7, 7>$ onto $< - 3, 4, - 5 >$ $< -3 , 4, -5>$ ?