Q104 / 160 · AP EAMCET 2020 (18 Sep Shift 2) · Mathematics

Let \(u\) and \(v\) be two non zero vectors, if \(|u+v|=|u-v|\), then

  • A
    \(u\) and \(v\) have the same direction
  • Correct answer
    B
    \(u\) and \(v\) are perpendicular
  • C
    \(u\) and \(v\) have the opposite direction
  • D
    Data Insufficient

Solution

\(|\mathrm{u}+\mathrm{v}|=|\mathrm{u}-\mathrm{v}|\) Squaring on both sides, \(\begin{aligned} |\mathrm{u}+\mathrm{v}|^2 & =|\mathrm{u}-\mathrm{v}|^2 \\ |\mathrm{u}|^2+|\mathrm{v}|^2+\overline{\bar{u} v} & =|\mathrm{u}|^2+|\mathrm{v}|^2+2(\bar{u} v) \\ 4(\bar{u} \cdot \bar{v}) & =0 \\ \bar{u}, v & =0 \\ \bar{u} & \perp \bar{v} \end{aligned}\) Hence, option (b) is correct.

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

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