Answer to Question #29446 in Electricity and Magnetism for Akarsh Anupam

Question

Express the magnitudes of aXb in terms of scalar products.

Answer 1

If a and b are vectors, and aXb is their vector product, themagnitude of it is
abs(aXb) = abs(a)*abs(b)*sin(a,b), where (a,b) is the anglebetween the vectors a and b.
If a.b is the scalar product of these two vectors, it is a.b= abs(a)*abs(b)*cos(a,b),
and the magnitude of the vector product is
abs(aXb) = (a.b) * sin(a,b) / cos(a,b) = (a.b) *tan(a,b).