Q52 / 150 · MHT CET 2008 · Mathematics

If $\overrightarrow{\mathbf{a}} \cdot \hat{\mathbf{i}}=4$, then $(\overrightarrow{\mathbf{a}} \times \hat{\mathbf{j}}) \cdot(2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}})$ is equal to

  • A
    12
  • B
    2
  • C
    0
  • Correct answer
    D
    $-12$

Solution

$(\overrightarrow{\mathbf{a}} \times \hat{\mathbf{j}}) \cdot(2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}})=\overrightarrow{\mathbf{a}} \cdot\{\hat{\mathbf{j}} \times(2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}})\}$ $$ \begin{array}{l} =\overrightarrow{\mathbf{a}} \cdot\{-3(\hat{\mathbf{j}} \times \hat{\mathbf{k}})\} \\ =-3(\overrightarrow{\mathbf{a}} \cdot \hat{\mathbf{i}}) \\ =-12 \quad(\because \overrightarrow{\mathbf{a}} \cdot \hat{\mathbf{i}}=4 \text { given }) \end{array} $$

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

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