Mathematics

Problem

Identify the geometrical quantity represented by

\lvert \mathbf{a}\times \mathbf{b} \rvert

, where

\mathbf{a}

and

\mathbf{b}

are non-collinear vectors. a) Area of the triangle formed by

\mathbf a

and

\mathbf b

b) Area of the rectangle having side lengths

|\mathbf a|

and

|\mathbf b|

c) Area of the parallelogram with

\mathbf a

and

\mathbf b

as adjacent sides d) Area of the parallelogram with sides

2\mathbf a

and

\mathbf b