Q83 / 160 · AP EAMCET 2020 (21 Sep Shift 2) · Mathematics

Let \(\mathbf{u}=-2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}\) and \(\mathbf{v}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}\). Then the component of \(\mathbf{v}\) on \(\mathbf{u}\) is

  • A
    \(\frac{4}{3}\)
  • Correct answer
    B
    \(\frac{-4}{3}\)
  • C
    \(\frac{-2}{3}\)
  • D
    \(\frac{2}{3}\)

Solution

Given vectors are \(\mathbf{u}=-2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}\) and \(\mathbf{v}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}\) \(\therefore\) Component of \(\mathbf{v}\) on \(\mathbf{u}\) is \(=\frac{\mathbf{v} \cdot \mathbf{u}}{|\mathbf{u}|}=\frac{-2-4+2}{\sqrt{4+4+1}}=\frac{-4}{3}\) Hence, option (b) is correct.

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

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