The area of the parallelogram having diagonal | vedclass

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Question

Here $a=3 i+j-2 k, b=i-3 j+4 k$

Thus $a 	imes b =\left|\begin{array}{ccc} i & j & k \ 3 & 1 & -2 \ 1 & -3 & 4\end{array}

Vedclass · Accepted Answer

${\rm{5}}\sqrt {\rm{3}}$

Vedclass · Answer

Here $a=3 i+j-2 k, b=i-3 j+4 k$

Thus $a 	imes b =\left|\begin{array}{ccc} i & j & k \ 3 & 1 & -2 \ 1 & -3 & 4\end{array}ight|$$=-2 i-14 j-10 k =-2(i+7 j +5 k )$

Hence area of parallelogram $=\frac{1}{2}| a 	imes b |=5 \sqrt{3}$

The area of the parallelogram having diagonals ${3\hat i}\,\, + \,\,\hat j\,\, - \,\,2\hat k$ and $\hat i\,\, - \,\,3\hat j\,\, + \;\,4\hat k$ is

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