What is the projection of <0,8,5><0,8,5> onto <1,2,-4><1,2,−4>?

1 Answer
Chitram Banerjee
Apr 26, 2016

-4/sqrt(21)−4√21

Explanation:

The projection of a vector AA along a direction thetaθ with itself is given as |A|costheta|A|cosθ

Lets say here A = <0,8,5>A=<0,8,5>
And B = <1,2,-4>B=<1,2,−4>

Their dot product is |A| |B| costheta = 0+16-20 =-4|A||B|cosθ=0+16−20=−4

So the projection is (|A||B|costheta)/(|B|) = (-4)/sqrt(1^2+2^2+4^2) = -4/sqrt(21)|A||B|cosθ|B|=−4√12+22+42=−4√21

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