What is the projection of <−5,3,7> onto <0,8,−2>?

1 Answer
Narad T.
Nov 26, 2016

The projection is =⟨0,2017,−517⟩

Explanation:

Let →a=⟨0,8,−2⟩

and →b=⟨−5,3,7⟩

The projection of →b onto →a is

=→a.→b∥∥→a∥∥2→a

Let's calculate the dot product

→a.→b=⟨0,8,−2⟩.⟨−5,3,7⟩=0⋅−5+8⋅3⋅−2⋅7=0+24−14=10

Then, we calculate the modulus of →a

∥∥→a∥=∥⟨0,8,−2⟩∥=√0+64+4=√68

The ptojection is =1068⟨0,8,−2⟩=534⟨0,8,−2⟩

=⟨0,4034,−1034⟩

=⟨0,2017,−517⟩

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