How can I find the magnitude of a vector B when I know the unit vector B, the vector A and the result cross product of AXB?

In other words, in a 2D plane, I know the final torque( A X B) on the k (out of the plane), I know the vector A (arm),

I know the direction the B is (the direction of the force) but I do not know the magnitude of that force

I am stuck, any help please?

Thank you!

Answer 1

[Torsten]

Calculate

A x B_unit 

Then the magnitude of B is

m = norm(A x B)/norm(A x B_unit)

where B_unit is the unit vector in the direction of the force.

[Emmanouil Karamousadakis]

Thank you for your reply, but on here

m = norm(A x B)/norm(A x B_unit)

I do know B_unit, but not B. Im I missing something?

[Torsten]

Yes, you miss that you said you know A x B.

[Emmanouil Karamousadakis]

Thank you, it worked fine!

Answer 2

[Jon]

Lets say you have the final Torque, and arm as a three element vectors T, and A respectiviely. Then I think the magnitude of the force would be

F = norm(T)/norm(A)