What is the projection of <8,−1,6> onto <−1,5,−3>?

1 Answer
Narad T.
Oct 21, 2016

The vector projection is ⟨−3135,−317,9335⟩

Explanation:

Let →b=⟨8,−1,6⟩

and →a=⟨−1,5,−3⟩

Then the vector projection of →b onto →a is
=→a.→b(∣→a∣)2⋅→a
where the dot product is →a.→b

dot product (8⋅−1)+(−1⋅5)+(6⋅−3)=−8−5−18=−31

and (∣→a∣)2=(1+25+9)=35

so the projection is −3135⟨−1,5,−3⟩=⟨−3135,−317,9335⟩

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