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?

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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!
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Torsten il 18 Lug 2022
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.
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Torsten il 18 Lug 2022
Yes, you miss that you said you know A x B.
Emmanouil Karamousadakis il 18 Lug 2022
Thank you, it worked fine!

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Jon il 18 Lug 2022
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)
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