Q49 / 90 · JEE Main 2013 (09 Apr Online) · Mathematics

The vector $(\hat{i} \times \vec{a} \cdot \vec{b}) \hat{i}+(\hat{j} \times \vec{a} \vec{b}) \hat{j}+(\hat{k} \times \vec{a} \cdot \vec{b}) \hat{k}$ is equal to:

  • A
    $\vec{b} \times \vec{a}$
  • B
    $\vec{a}$
  • Correct answer
    C
    $\vec{a} \times \vec{b}$
  • D
    $\vec{b}$

Solution

$(\hat{i} \times \vec{a} \cdot \vec{b}) \hat{i}+(\hat{j} \times \vec{a} \cdot \vec{b}) \hat{j}+(\hat{k} \times \vec{a} \cdot \vec{b}) \hat{k}$ $=(\hat{i} \cdot \vec{a} \times \vec{b}) \hat{i}+(\hat{j} \cdot \vec{a} \times \vec{b}) \hat{j}+(\hat{k} \cdot \vec{a} \times \vec{b}) \hat{k}$ $(\because \vec{a} \times \vec{b} \cdot \vec{c}=\vec{a} \cdot \vec{b} \times \vec{c})$ $=(\vec{a} \times \vec{b}) \hat{i}+(\vec{a} \times \vec{b}) \hat{j}+(\vec{a} \times \vec{b}) \hat{k}$ $==\vec{a} \times \vec{b}$

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

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