What is the projection of <−7,3,−5> onto <4,−5,1>?

1 Answer
Narad T.
Nov 7, 2016

The projection =⟨−327,407,−87⟩

Explanation:

The projection of →b onto →a is given by
=→a.→b∥∥→a∥⋅∥→a∥∥→a

The dot product is
→a.→b=⟨−7,3,−5⟩.⟨4,−5,1⟩=−28−15−5=−48

The modulus of →a =∥→a∥=∥⟨4,−5,1⟩∥=√16+25+1=√42

The projection is =−4842⟨4,−5,1⟩=−87⟨4,−5,1⟩

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