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

any help with this one please.

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- March 6th 2007, 11:06 PMrcmangocross products
Find the cross product of the vectors i + j - k and i - j + k

any help with this one please. - March 7th 2007, 12:18 AMJameson
This is pretty standard. Do you know the formula for the cross product of two vectors?

- March 7th 2007, 06:35 AMAfterShock
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.