Question

(URGENT)use the vectors to determine two dot products​

Answer 1

u = 9 i - 6 j

v = -3 i - 2j

w = 19 i + 15 j

u • v = (9 i - 6 j) • (-3 i - 2j)

Distribute the dot products:

u • v = 9*(-3) (i • i) + 9*(-2) (i • j) + (-6)*(-3) (j • i) + (-6)*(-2) (j • j)

i and j are orthogonal unit vectors, so their dot products are 0, while i • i = j • j = 1. So we have

u • v = 9*(-3) + (-6)*(-2) = -27 + 12 = -15

In other words, the dot product can be computed by simply multiplying corresponding components, and taking the total.

u • w = 9*19 + (-6)*15 = 81