(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the projection of P in the direction of Q and the component of P orthogonal to Q.

P=i-3j+k Q=-i+2j+5k

2. Relevant equations

Proj_{Q}(P)={(P*Q)/(Q*Q)}Q

Orth_{Q}(P)=P-Proj_{Q}(P)

3. The attempt at a solution

First I get P=(1,-3,1) and Q=(-1,2,5)

Proj_{Q}(P)

=(-2/30)*(-1,2,5)

={(1/15),(-2/15),(-1/3)}

That's correct, as far as the book is concerned.

Now, finding the orthogonal part is where I get held up.

I do this:

Orth_{Q}(P)=

=(1,-3,1)-{(1/15),(-2/15),(-1/3)}

={14/15,(47/15),(4/3)}

Which is wrong. The book says the correct answer is: {(74/15),(32/15),(-2/3)}.

I'm at a complete loss as to how they got this. Any help is much appreciated.

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# Homework Help: Vector Calc: Ortho Projections

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