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9 February, 07:40

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

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Answers (1)
  1. 9 February, 07:46
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    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)
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