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?

littlemixfan Oct 16, 2020

#1

#2**+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**+3 **

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

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

**v**•**u** = |v|*|u|*cos(theta) = **u•v**

The same is true for the other dot products.

Alan
Oct 16, 2020

#5