# Math Help - cross products

1. ## cross products

Find the cross product of the vectors i + j - k and i - j + k

any help with this one please.

2. This is pretty standard. Do you know the formula for the cross product of two vectors?

3. Originally Posted by rcmango
Find the cross product of the vectors i + j - k and i - j + k

any help with this one please.
Let a = <1, 1, -1>, b = <1, -1, 1>

Then,

a x b = [[0, -a_3, a_2], [a_3, 0, -a_1], [-a_2, a_1, 0]]*[[b_1], [b_2], [b_3]], where the * is matrix multiplication.

And thus we have:

a x b = [[0, 1, 1], [-1, 0, -1], [-1, 1, 0]]*[[1], [-1], [1]]

= <0, -2, 0>

You can also compute the cross product using determinants, which some people find easier. I personally find this much faster.