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Question: If vector $a = <2,3,5>$ and vector $b = <2,-2,-1>$, find the vector projection of b onto a and hence find the component of b perpendicular to a.

I found the vector projection of b onto a using the vector projection formula which is (-7/38)<2,3,5>.

Do I find the component of b perpendicular to a by using vector b - vector projection? Would this be <2,-2,-1> - (-7/38)<2,3,5>?

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Vector Projection = $\mbox{proj}_{a}b=\dfrac{a\cdot b}{|a|^2}a=\dfrac{\langle2,3,5\rangle\langle2,-2,-1\rangle}{38}(2)$

The component of b perpendicular to a is $b-\mbox{proj}_{a}b$

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  • $\begingroup$ @llamaro25 If you find my answer helpful then accept the answer $\checkmark$ :) $\endgroup$ – Key Flex Mar 25 at 13:27

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