Q206 / 270 · NDA 2011 (Phase 1) · Mathematics

What is the projection of the vector $\hat{i}-2 \hat{j}+\hat{k}$ on the vector $4 \hat{i}-4 \hat{j}+7 \hat{k}$ ?

  • A
    $\frac{\sqrt{5}}{2}$
  • Correct answer
    B
    $\frac{19}{9}$
  • C
    $\frac{\sqrt{5}}{4}$
  • D
    $\frac{11}{3}$

Solution

Projection of the vector $\hat{i}-2 \hat{j}+\hat{k}$ on the vector $\begin{aligned} 4 \hat{i}-4 \hat{j}+7 \hat{k} & =\frac{(\hat{i}-2 \hat{j}+\hat{k}) \cdot(4 \hat{i}-4 \hat{j}+7 \hat{k})}{|4 \hat{i}-4 \hat{j}+7 \hat{k}|} \\ & =\frac{4+8+7}{\sqrt{16+16+49}}=\frac{19}{\sqrt{81}}=\frac{19}{9} . \end{aligned}$

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

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