Question

Three concurrent edges OA, OB, OC of a parallelopiped are represented by three vectors $2\mathbf{i} + \mathbf{j} - \mathbf{k},\mathbf{i} + 2\mathbf{j} + 3\mathbf{k}$ and $- 3\mathbf{i} - \mathbf{j} + \mathbf{k},$ the volume of the solid so formed in cubic unit is

• A. 5
• B. 6
• C. 7
• D. 8

Answer 1

Answer: (A)

5

Answer 2

Vol. of parallelopiped $= \left| \begin{matrix} \mathbf{a}{1} & \mathbf{b}{1} & \mathbf{c}{1} \ \mathbf{a}{2} & \mathbf{b}{2} & \mathbf{c}{2} \ \mathbf{a}{3} & \mathbf{b}{3} & \mathbf{c}_{3} \end{matrix} \right| = \left| \begin{matrix} 2 & 1 & - 1 \ 1 & 2 & 3 \

• 3 & - 1 & 1 \end{matrix} \right|$

$= 2(5) - 1(1 + 9) - 1(5) = | - 5| = 5$ cubic unit.