Question

Show that magnitude of vector product of two vectors is numerically equal to the area of a parallelogram formed by two vectors.

Answer 1

$Formulaforareaofparallelogram$

$=base\times height$

$=\left|\overline{a}\right|.h$

$h=\left|\overline{b}\right|\sin \theta$

$\therefore Area=\left|\overline{a}\right|.\left|\overline{b}\right|\sin \theta$

$Weknow|\overline{a}\times \overline{b}|=\left|\overline{a}\right|.\left|\overline{b}\right|\sin \theta$

$Henceproved.$