+226 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?
+226 It would be
3(v•u) - 2(w•u) = -3(u•v) + 2(u•w) = -3x3 + 2x4 = -9 + 8 = -1
right?
+33657 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.
+226 So that would mean
the second one is 5-3 =2
the third is 9-8 = 1
right?
