Correct Answer - Option 3 : 23
Concept:
The volume of the parallelepiped determined by \(\rm \vec a,\text{ }\vec b\text{ and }\vec c\)is
Volume = \(\rm \vec a\cdot\left(\vec b\times\vec c\right)\) = \(\rm \begin{vmatrix} \rm a_1 & \rm a_2 & \rm a_3\\ \rm b_1 & \rm b_2 & \rm b_3\\ \rm c_1 & \rm c_2 & \rm c_3 \end{vmatrix}\)
Calculation:
Parallelepiped determined by:
u = i + 2j - k
v = -2i + 3k
w = 7j - 4k
Volume = \(\rm \begin{vmatrix} 1 & 2 & -1\\ -2 & 0 & 3\\ 0 & 7 & -4 \end{vmatrix}\)
⇒ Volume =\(\rm \left |1\times(0 - 21) - 2\times(8 - 0) + (-1)\times(-14-0)\right|\)
⇒ Volume =\(\rm \boldsymbol {\left |- 23\right|}\) = 23 units
