Question

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

Answer 1

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)