Question

The volume of the parallelopiped whose edges are represented by $- 12\mathbf{i} + \alpha\mathbf{k},3\mathbf{j} - \mathbf{k}$ and $2\mathbf{i} + \mathbf{j} - 15\mathbf{k}$ is 546. Then $\alpha =$

• A. 3
• B. 2
• C. – 3
• D. ­– 2

Answer 1

Answer: (C)

– 3

Answer 2

Since $\left| \begin{matrix}

• 12 & 0 & \alpha \ 0 & 3 & - 1 \ 2 & 1 & - 15 \end{matrix} \right| = 546 \Rightarrow \alpha = - 3.$