Q55 / 200 · AP EAMCET 2001 · Mathematics

$[\hat{\mathbf{i}}-\hat{\mathbf{j}}, \hat{\mathbf{j}}-\hat{\mathbf{k}}, \hat{\mathbf{k}}-\hat{\mathbf{i}}]$ is equal to

  • Correct answer
    A
    $0$
  • B
    $1$
  • C
    $2$
  • D
    $3$

Solution

$\begin{aligned} & {[\hat{\mathbf{i}}-\hat{\mathbf{j}} \cdot \hat{\mathbf{j}}-\hat{\mathbf{k}}, \hat{\mathbf{k}}-\hat{\mathbf{i}}]} \\ & =\left|\begin{array}{ccc}1 & -1 & 0 \\ 0 & 1 & -1 \\ -1 & 0 & 1\end{array}\right|=1(1-0)+1(0-1) \\ & =1-1=0 \\ & \end{aligned}$

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

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