The area of the parallelogram whose sides are represented by the vectors $\hat j + 3\hat k$ and $\hat i + 2\hat j - \hat k$ is
The area of the parallelogram whose sides are represented by the vectors $\hat j + 3\hat k$ and $\hat i + 2\hat j - \hat k$ is
$\sqrt {61} $ sq.unit
$\sqrt {59} $ sq.unit
$\sqrt {49} $ sq.unit
$\sqrt {52} $ sq.unit
The area of the parallelogram whose sides are represented by the vectors $\hat j + 3\hat k$ and $\hat i + 2\hat j - \hat k$ is
$\vec A = \hat j + 3\hat k$,$\vec B = \hat i + 2\hat j - \hat k$
$\vec C = \vec A \times \vec B = \left| {\,\begin{array}{*{20}{c}}{\hat i}&{\hat j}&{\hat k}\\0&1&3\\1&2&{ - 1}\end{array}\,} \right|$$ = - 7\hat i + 3\hat j - \hat k$
Hence area = $|\vec C| = \sqrt {49 + 9 + 1} = \sqrt {59} \,sq\,unit$