How can I algebraically manipulate a vector cross product?

Question

For instance, how would I go about solving for B in the following equation?

F = qV x B

Where q is a scalar, and V and B are vectors.

Answer 1

you can use the fact that B is orthogonal on V or use the brute force method : write it out and solvbe the system of equations you get

Answer 2

There are various identities to use; none of which I remember right now. Maybe this will help:

The F vector is perpendicular to the plane of the V and B vectors. The magnitude of F is :

|F| = q*|V|*|B|*sin (angle)

where angle is the angle between the B and V vectors. That should be enough information to solve for B.

Answer 3

solve them using 3 equations and 3 unknowns
Fx = q(Vy*Bz - Vz*By)
Fy = ...
Fz = ...
hard.. i think.. atleast this is solvable coz u have equal number of equations to the number of unknowns

Answer 4

We know that
|F| = q|V||B|sinθ
|B| = |F|/(q|V|sinθ.

The rub is that there is no way to back-calculate θ, given F, q, and V, so you can't solve for B unless θ is known.

Answer 5

I love it when people talk dirty!