Answer:
Option C
Explanation:
We have
AB= $(5-3)\hat{i}+(-2-7)\hat{j}+(3-4)\hat{k}$
= $2\hat{i}-9\hat{j}-\hat{k}$
AC= $(-4-3)\hat{i}+(5-7)\hat{j}+(6-4)\hat{k}$
= $-7\hat{i}-2\hat{j}+2\hat{k}$
and AD= $(1-3)\hat{i}+(2-7)\hat{j}+(6-4)\hat{k}$
= $-2\hat{i}-5\hat{j}-\hat{k}$
$\therefore$ Volume of the parallelopiped with AB,AC and AD on the co-terminus edges
$[(AB$ $AC$ $AD)]=\begin{bmatrix}2 & -9 &-1 \\-7 & -2 &2\\ -2&-5&-1 \end{bmatrix}$
=|2(2+10)+9(7+4)-1(35-4)|
=|2(12)+9(11)-1(31)|
=|(24+99-31)|
|92|=92 cubic unit
