Vector Cross Product Homework: Find 3rd Vector Perpendicular to C & D

[xcgirl]

Homework Statement

C= B|A| + A|B|
D= A|B|-B|A|
C and D are orthogonal
Find a third vector perpendicular to both C and D

Homework Equations

[AxB] = |A||B|sin(theta)

The Attempt at a Solution

I know that to find the answer I need to find the cross product of C and D. I have done similar problems, but the unit components (i,j,k) have always been given. I can't figure out a way to do this without having those.
Thanks for any help, even a hint!

 

[rl.bhat]

CXD = (B|A| + A|B|)X( A|B|-B|A|)
Do the cross multiplication of right hand side. Note that AXA = BXB = 0 And AXB = -BXA
You can multiply the magnitudes of A and B directly.

 

[xcgirl]

so I can do...

BxA|A||B| + BxB|A||A| + AxA|B||B| - AxB|B||A|
BxA|A||B| - AxB|B||A|

so would that be the final answer? thanks for the help, this all just seems a little weird to me. I didnt know that you could just essentially "foil" it like that

 

[rl.bhat]

Last step
CXD = 2(AB)*BXA, because AXB = BXB = 0

 

[xcgirl]

thanks, you're a lifesaver! i totally get it now