Question

Cross products?

Find the cross product of -3/4v and 1/2w if v=(-2,12,-3) and w=(-7,4,-6).
Please show work/explain!

Answer 1

`(45/2, -27/8, -57/2)`

Explanation:

So, let's simplify this by multiplying our -3/4's and 1/2's to the vectors v and w.

`-3/4v and 1/2w = (6/4, -9, 9/4), (-7/2, 2, -3)`

Alright, next we use the cross product formula of two vectors:

`(v_1, v_2, v_3)*(w_1, w_2, w_3) = (v_2w_3 - v_3w_2, v_3w_1 - v_1w_3, v_1w_2 - v_2w_1)`

Substituting our vectors we get:

`(-9(-3) - 9/4*2, 9/4(-7/2)-6/4(-3), 6/4*2-(-9(-7/2)))`

After completing our operations, we get:

`(45/2, -27/8, -57/2)`

~ Alex