Let v1 = (-6,4) and v2 = (-3,6) compute the following.

a. V1*V2

b. The angle between |v1| and |V2|.

c. The scaler projection of v1 onto v2

d. the projection of v1 onto v2

a. We assume you want the dot product. That is the sum of the products of the corresponding components.

... V1•V2 = (-6) (-3) + (4) (6) = 18 + 24 = 42

b. V1•V2 = |V1|·|V2|·cos (α)

... α = arccos (V1•V2 / (|V1|·|V2|)

... α = arccos (42/√ (((-6) ²+4²) ((-3) ²+6²)))

... α = arccos (42/√2340)

... α ≈ 29.74°

c. The scalar projection of V1 onto V2 is the dot product of V1 with the unit vector in the V2 direction.

... V1•V2/|V2| = 42/√45 = 42 / (3√5) = (14/5) √5

d. The projection of V1 onto V2 is the result of part c multiplied by the unit vector in the direction of V2.

... projection of V1 onto V2 = (14/5) √5· (-3, 6) / (3√5) = (14/5) (-1, 2) = (-14/5, 28/5)