Two-dimensional collision with two moving objects formula for velocity

Question

Could anyone explain me this formula?

$$\langle \mathbf v_1 - \mathbf v_2, \mathbf x_1 - \mathbf x_2 \rangle =\ ?$$ $$\left\|\mathbf x_1 - \mathbf x_2\right\|^2 =\ ?$$

Well, I know that... I want to know about this: <v1 - v2, x1 - x2> = ?, and this: ||x1 - x2||^2 = ?... — Collision, Jun 14 '16 at 18:59
I guess it pops out when you require conservation of energy and momentum. — , Jun 14 '16 at 19:02

score 2 · Accepted Answer · edited Jun 14 '16 at 19:09

2

I guess $\langle a,b\rangle$, where $a,b\in\mathbb{R}^n$, refers to the scalar product.

Regarding $\|a\|^2$, I suppose it is the corresponding norm: $\|a\|^2=\langle a,a\rangle$.

edited Jun 14 '16 at 19:09

Arthur

answered Jun 14 '16 at 19:05

AugSB

So <v1 - v2, x1 - x2> = (v1.x - v2.x) * (x1.x - x2.x) + (v1.y - v2.y) * (x1.y - x2.y) + (v1.z - v2.z) * (x1.z - x2.z)? – Collision Jun 14 '16 at 19:08
@Collision Yes. – Arthur Jun 14 '16 at 19:09
Yes, that's it! – AugSB Jun 14 '16 at 19:10

1 Answers1