If are mutually perpendicular, show that Is the converse true?
Given:
, and are mutually perpendicular.
A×B is a vector with its direction perpendicular to the plane containing and .
∴ The angle between
and × is either 0° or 180°.
i.e., =0
However, the converse is not true. For example, if two of the vectors are parallel, then also,
=0
So, they need not be mutually perpendicular.