extremely hard question

Question

Let vector x = (5, −3) and vector y = (−1, 2).

Compute   comp_{vector x}(vector y).

Answer 1

Recall that the formula: comp_x y = (x·y) / ||x||.

 

For your case we have:

 

x·y = ⟨5,-3⟩·⟨-1,2⟩ = (5)(-1)+(-3)(2) = (-5)+(-6) = -11

 

||x|| = || ⟨5,-3⟩ || = √(5²+(-3)²) = √34

 

comp_x y = -11 / √34 ≈ -1.886