+0

0
32
5
+199

Let u,v and w be vectors satisfying $$\mathbf{u}\bullet \mathbf{v} = 3, \mathbf{u} \bullet \mathbf{w} = 4, \mathbf{v} \bullet \mathbf{w} = 5.$$
Then what are $$(\mathbf{u} + 2 \mathbf{v})\bullet \mathbf{w}, (\mathbf{w} - \mathbf{u})\bullet \mathbf{v}, (3\mathbf{v} - 2 \mathbf{w})\bullet \mathbf{u}$$ equal to?

Oct 16, 2020

#1
+31093
+2

(u + 2v)•w = u•w + 2*v•w = 4 + 2*5 = 14

Oct 16, 2020
edited by Alan  Oct 16, 2020
#2
+199
+1

It would be

3(v•u) - 2(w•u) = -3(u•v) + 2(u•w) = -3x3 + 2x4 = -9 + 8 = -1

right?

littlemixfan  Oct 16, 2020
#4
+31093
+1

Apologies, I've misled you by reacting too quickly, with too little thought!

With dot products  uv = |u|*|v|*cos(theta), where |u| is the magnitude of u, and theta is the angle between u and v. This means that

vu = |v|*|u|*cos(theta) = u•v

The same is true for the other dot products.

Alan  Oct 16, 2020
#5
+199
+1

So that would mean

the second one is 5-3 =2

the third is 9-8 = 1

right?

littlemixfan  Oct 16, 2020