Q109 / 180 · KCET 2024 · Mathematics

The volume of the parallelopiped whose co terminous edges are $\hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{i}}+\hat{\mathbf{k}}$ and $\hat{\mathbf{i}}+\hat{\mathbf{j}}$ is

  • A
    6 cu units
  • Correct answer
    B
    2 cu units
  • C
    4 cu units
  • D
    3 cu units

Solution

The volume of the parallelopiped whose coterminous edges are $\hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{i}}+\hat{\mathbf{k}}$ and $\hat{\mathbf{i}}+\hat{\mathbf{j}}=\left|\begin{array}{lll}0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0\end{array}\right|$ $=0-1(0-1)+1(1-0)$ $=-1(-1)+1$ $=2 \mathrm{cu}$ units

Hence, the correct answer is option: 'B'.

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