What is the projection of $< - 8, 3, 7 >$ $<-8,3,7 >$ onto $< 1, 4, - 3 >$ $<1,4,-3 >$ ?

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What is the projection of $< - 8, 3, 7 >$ $<-8,3,7 >$ onto $< 1, 4, - 3 >$ $<1,4,-3 >$ ?

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Answer 1 · 2016-02-14T18:01:22

$\to c = < \frac{17}{26}, \frac{68}{26}, - \frac{51}{26} >$ $vec c=<17/26,68/26,-51/26>$

Explanation:

$\to a = < - 8, 3, 7 >$ $vec a= <-8,3,7>$
$\to b = < 1, 4, - 3 >$ $vec b= <1,4,-3>$
$\to c = \frac{\to a \cdot \to b}{| b | . | b |} \cdot \to b$ $vec c= (vec a*vec b)/(|b|.|b|)*vec b$
$\to a \cdot \to b = - 8 \cdot 1 + 3 \cdot 4 - 3 \cdot 7 = - 8 + 12 - 21 = - 17$ $vec a*vec b=-8*1+3*4-3*7=-8+12-21=-17$
$∣ ∣ ∣ \to b ∣ ∣ ∣ = \sqrt{1^{2} + 4^{2} {(- 3)}^{2}} = \sqrt{26}$ $|vec b|=sqrt(1^2+4^2(-3)^2)=sqrt 26$
$\to c = - \frac{17}{\sqrt{26} \cdot \sqrt{26}} \cdot < 1, 4, - 3 >$ $vec c=-17/(sqrt 26*sqrt 26)*<1,4,-3>$
$\to c = - \frac{17}{26} < 1, 4, - 3 >$ $vec c=-17/26<1,4,-3>$
$\to c = < \frac{17}{26} \cdot 1, \frac{17}{26} \cdot 4, - \frac{17}{26} \cdot 3 >$ $vec c=<17/26*1,17/26*4,-17/26*3>$
$\to c = < \frac{17}{26}, \frac{68}{26}, - \frac{51}{26} >$ $vec c=<17/26,68/26,-51/26>$

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What is the projection of $< - 8, 3, 7 >$ $<-8,3,7 >$ onto $< 1, 4, - 3 >$ $<1,4,-3 >$ ?

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Explanation:

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What is the projection of <−8,3,7><-8,3,7 > onto <1,4,−3><1,4,-3 >?

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Explanation:

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What is the projection of $< - 8, 3, 7 >$ $<-8,3,7 >$ onto $< 1, 4, - 3 >$ $<1,4,-3 >$ ?