Its actually not so much the cross product itself that's giving me trouble but sorting out the algebra that follows. The problem is as follows:

There are two vectors U and V such that UxV = -30i + 40j. V= 4i -2j +3k, find U.

Using U = U_{x}i + U_{y}j + U_{z}k, I get: UxV= (3U_{y}+ 2U_{z})i - (3U_{x}- 4U_{z})j + (-2U_{x}- 4U_{y})k,

and, therefore:

3U_{y}+ 2U_{z}= -30 (eqn 1)

-3U_{x}+ 4U_{z}= 0 (eqn 2)

-2U_{x}- 4U_{y}= 40 (eqn 3)

So far so good, I hope. No is where I come into trouble. Instead of solving the three eqns for the three unknowns, I end up with 0=0. Which, though I'm glad is true, is of no use to me. My math is as follows:

From eqn 2, U_{x}= 4/3 U_{z}

From previous and eqn 3, -8/3 Uz -4U_{y}= 40 => U_{z}= -3/2 U_{y}- 15

From previous and eqn 1, 3U_{y }-3U_{y }-30 = -30 => 0=0

If you see my error, please let me know.

Thanks much.

j

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