The magnitude of the scalar product of vectors A and B is three times as large as the magnitude of the vector product of the same two vectors. If they were placed tail-to-tail in space, A and B would form an angle of approximately how much?

Question

The magnitude of the scalar product of vectors A and B is three times as large as the magnitude of the vector product of the same two vectors.  If they were placed tail-to-tail in space, A and B would form an angle of approximately how much?

MathMate · Answer

The magnitude of AxB is C=|A||B|sinθ while the magnitude of A.B is D=|A||B|cosθ So if D/C=3 => cotθ=3 Solve for θ