Hello,

I seem to have forgotten how to solve this type of problem as even by constructing vectors from random number, getting their cross product, substituting one vector with dummy variable and attempting to solve for the vector, I keep getting trivial solutions. Can someone please explain what I'm doing wrong. Here is an example:

U = 1i +2j +3k

V = 4i +5j +6k

UxV = (12-15)i - (6-12)j + (5-8)k = -3i +6j -3k

Now use V and UxV to find U:

let U = ai + bj + ck

UxV = (6b - 5c)i - (6a - 4c)j + (5a - 4b)k

Gives the following system:

6b - 5c = -3 (1)

-6a + 4c = 6 (2)

5a - 4b = -3 (3)

From (1): b = 5c/6 - 1/2

from (2): a = 2c/3 - 1

Plugging into (3): 10c/3 - 5 - 10c/3 +2 = -3

-3 = -3

I run into something similar whether its a made up problem or one from a text that's designed to be solveable. Any help is much appreciated.

J