Q59 / 120 · VITEEE 2011 · Mathematics

The projection of the vector $\boldsymbol{i}-2 \boldsymbol{j}+\boldsymbol{k}$ on the vector $4 i-4 j+7 k$ is

  • A
    $\frac{5 \sqrt{6}}{10}$
  • Correct answer
    B
    $\frac{19}{9}$
  • C
    $\frac{9}{19}$
  • D
    $\frac{\sqrt{6}}{19}$

Solution

Let $\mathbf{a}=\mathbf{i}-2 \mathbf{j}+\mathbf{k}$ and $\mathbf{b}=4 \mathbf{i}-4 \mathbf{j}+7 \mathbf{k}$, then projection of $\mathbf{a}$ on $\mathbf{b}$ is equal to $$ \frac{\text { a.b }}{|\mathbf{b}|}=\frac{4+8+7}{\sqrt{16+16+49}}=\frac{19}{9} $$

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

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