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winowmak3r
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Homework Statement
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
Homework Equations
ProjQ(P)={(P*Q)/(Q*Q)}Q
OrthQ(P)=P-ProjQ(P)
The Attempt at a Solution
First I get P=(1,-3,1) and Q=(-1,2,5)
ProjQ(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:
OrthQ(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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