Find the scalar and vector projection of the vector 𝐛=⟨5,5,−5⟩ onto the vector 𝐚=⟨5,0,−5⟩.

Question

Determine Scalar projection (i.e., component): 

Vector projection 

 

Answer 1

Scalar projection proj_ab = (a•b)/IaI = (5·5 + 5·0 +(- 5)(- 5))/√(5² + 0² + (- 5)²) = 50/√50 = 5√2

Vector projection proj_ab = (a•b)a/IaI² = 5√2<5, 0, - 5>/5√2 = <5, 0, - 5>