Question 1109721: Use the vectors u = <2, 2>, v = <-3, 4> and w = <1, -2> to find the indicated quantity.
a. 3u ∙ v
b. (u ∙ 2v)w
Thanks!
Found 2 solutions by math_helper, rothauserc:
Answer by math_helper(2461)   (Show Source):
You can put this solution on YOUR website!
Using unit vectors i, j for x, y, components respectively:
a) 3u ∙ v = 3*(2i+2j) ∙ (-3i+4j) = (6i+6j) ∙(-3i+4j) = (6*(-3)) + (6*4) = -18 + 24 = 6
b) (u ∙ 2v)w — Follow the above procedure for (u ∙ 2v) then take the resulting number and multiply it by the two components of w.
Answer by rothauserc(4718)  (Show Source):
You can put this solution on YOUR website! Assumption is that vectors u, v, w start at the origin(0,0)
:
Looks like the problem is asking for the dot product, a · b = ax × bx + ay × by
:
a) 3u = 3<2,2> = <6,6>
3u · v = <6,6> · <-3,4> = -18 + 12 = -6
:
b) 2v = 2<-3,4> = <-6,8>
u · 2v = <2,2> · <-6,8> = -12 + 16 = 4
4w = 4<1,-2> = <4,-8>
:
|
|
|
