# How do you prove that a=-(w^2)

1. Feb 6, 2006

### asdf1

how do you prove that a=-(w^2)
from v=wxr?
i know you're supposed to differentiate v=wxr, but i don't know how to differentiate a cross product...

Last edited by a moderator: Jan 7, 2014
2. Feb 6, 2006

### scholzie

The cross product is the vector created by the determinant
$$a \times b = \begin{tabular}{|c c c|} i & j & k \\ a_1 & a_2 & a_3 \\ b_1 & b_2 & b_3 \\ \end{tabular}$$

So, take the determinant of the above matrix, and then differentiate as normal. (Hint: the determinant will give you a vector, with 3 coordinates. You can differentiate each coordinate on its own.)

Edit: are you familiar with how to take a determinant? Otherwise you can use $a \times b = |a||b|\sin{\theta}$, but then you'll have to know $\theta$, or treat it as a constant.

Last edited: Feb 6, 2006
3. Feb 7, 2006

### asdf1

wow!
thank you very much!!!
what happens if you want to prove it for an infinite number of coordinates(ex., i, j, k, l, m, ....)?

4. Feb 7, 2006

### HallsofIvy

Staff Emeritus
The cross product is only defined in R3.