Q208 / 270 · NDA 2015 (Phase 2) · Mathematics

The direction ratios of the line perpendicular to the lines with direction ratios $ \lt 1,-2,-2 \gt $ and $ \lt 0,2,1 \gt $ are

  • Correct answer
    A
    $ \lt 2,-1,2 \gt$
  • B
    $\langle-2,1,2\rangle$
  • C
    $\langle 2,1,-2\rangle$
  • D
    $\langle-2,-1,-2\rangle$

Solution

Let the direction ratio be $ \lt \mathrm{a}, \mathrm{b}, \mathrm{c} \gt $ $\begin{aligned} & \cos 90^{\circ}=\frac{(a)(1)+(b)(-2)+(c)(-2)}{\sqrt{\mathrm{a}^2+\mathrm{b}^2+\mathrm{c}^2} \sqrt{(1)^2+(-2)^2+(-2)^2}} \\ & \mathrm{a}-2 \mathrm{~b}-2 \mathrm{c}=0....(1) \\ & \cos 90^{\circ}=\frac{(\mathrm{a})(0)+\mathrm{b}(2)+(\mathrm{c})(1)}{\sqrt{\mathrm{a}^2+\mathrm{b}^2+\mathrm{c}^2} \sqrt{(0)^2+(-2)^2+(1)^2}} \\ & 2 \mathrm{~b}+\mathrm{c}=0....(2) \end{aligned}$ From eq. (1) \& (2) $\mathrm{a}=-2 \mathrm{~b} ; \mathrm{c}=-2 \mathrm{~b}$

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

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