Q214 / 270 · NDA 2015 (Phase 2) · Mathematics

If the position vector $\vec{a}$ of the point $(5, \mathrm{n})$ is such that $|\vec{a}|=13$, then the value/values of $n$ an be

  • A
    $\pm 8$
  • Correct answer
    B
    $\pm 12$
  • C
    8 only
  • D
    12 only

Solution

$\begin{aligned} & \sqrt{(5-0)^2+(\mathrm{n}-0)^2}=13 \\ & 25+\mathrm{n}^2=169 \\ & \mathrm{n}^2=144 \\ & \mathrm{n}= \pm 12\end{aligned}$

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

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