Q73 / 150 · MHT CET 2012 · Mathematics

$\mathbf{i} \cdot(\mathbf{j} \times \mathbf{k})+\mathbf{j} \cdot(\mathbf{k} \times \mathbf{i})+\mathbf{k} \cdot(\mathbf{j} \times \mathbf{i})$ is equal to

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

Solution

Given, $\begin{aligned} \mathbf{i} \cdot(\mathbf{j} \times \mathbf{k}) &+\mathbf{j} \cdot(\mathbf{k} \times \mathbf{i})+\mathbf{k} \cdot(\mathbf{j} \times \mathbf{i}) \\=& \mathbf{i} \cdot(\mathbf{i})+\mathbf{j} \cdot(\mathbf{j})+\mathbf{k} \cdot(-\mathbf{k}) \\=&(\mathbf{i} \cdot \mathbf{i})+(\mathbf{j} \cdot \mathbf{j})-(\mathbf{k} \cdot \mathbf{k}) \\=& 1+1-1=1 \end{aligned}$

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

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