Let 𝑎⃗ and 𝑏 be two vectors in the xy plane making angles 𝜃 and ∅ with the x axis, respectively.

Question

Use vector algebra to show that:
cos(𝜃 − ∅) = cos 𝜃 cos ∅ + sin 𝜃 sin ∅

Answer 1

The angle between a and b is α = θ-Ø

a•b = |a| |b| cosα

a•b = (xa*xb)+(ya*yb)
xa = |a| cosθ
ya = |a| sinθ
...
Carry on, and you will see the result fall right out.

Answer 2

good