Q85 / 200 · Manipal (MET) 2013 · Mathematics

If the scalar projection of the vector $x \mathbf{i}-\mathbf{j}+\mathbf{k}$ on the vector $2 \mathbf{i}-\mathbf{j}+5 \mathbf{k}$ is $\frac{1}{\sqrt{30}}$ then value of $x$ is equal to

  • Correct answer
    A
    $\frac{-5}{2}$
  • B
    $6$
  • C
    $-6$
  • D
    $3$

Solution

Projection of $\mathbf{x i}-\mathbf{j}+\mathbf{k}$ on $2 \mathbf{i}-\mathbf{j}+5 \mathbf{k}$ $=\frac{(x i-j+k) \cdot(2 i-j+5 k)}{\sqrt{4+1+25}}=\frac{2 x+1+5}{\sqrt{30}}$ But, given, $\frac{2 x+6}{\sqrt{30}}=\frac{1}{\sqrt{30}}$ $\begin{array}{rrr}\Rightarrow & 2 x+6=1 \\ \Rightarrow & x=\frac{-5}{2}\end{array}$

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

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