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 = Uxi + Uyj + Uzk, I get: UxV= (3Uy + 2Uz)i - (3Ux - 4Uz)j + (-2Ux - 4Uy)k,
and, therefore:
3Uy + 2Uz = -30 (eqn 1)
-3Ux + 4Uz = 0 (eqn 2)
-2Ux - 4Uy = 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, Ux = 4/3 Uz
From previous and eqn 3, -8/3 Uz -4Uy = 40 => Uz = -3/2 Uy - 15
From previous and eqn 1, 3Uy -3Uy -30 = -30 => 0=0
If you see my error, please let me know.
Thanks much.
j
There are two vectors U and V such that UxV = -30i + 40j. V= 4i -2j +3k, find U.
Using U = Uxi + Uyj + Uzk, I get: UxV= (3Uy + 2Uz)i - (3Ux - 4Uz)j + (-2Ux - 4Uy)k,
and, therefore:
3Uy + 2Uz = -30 (eqn 1)
-3Ux + 4Uz = 0 (eqn 2)
-2Ux - 4Uy = 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, Ux = 4/3 Uz
From previous and eqn 3, -8/3 Uz -4Uy = 40 => Uz = -3/2 Uy - 15
From previous and eqn 1, 3Uy -3Uy -30 = -30 => 0=0
If you see my error, please let me know.
Thanks much.
j