Q214 / 270 · NDA 2022 (Phase 2) · Mathematics

A plane cuts intercepts 2,2,1 on the coordinate axes. What are the direction cosines of the normal to the plane?

  • A
    $ \lt 2 / 3,2 / 3,1 / 3\rangle$
  • B
    $ \lt 1 / 3,2 / 3,2 / 3\rangle$
  • Correct answer
    C
    $\left\langle\frac{1}{\sqrt{6}}, \frac{1}{\sqrt{6}}, \frac{2}{\sqrt{6}}\right\rangle$
  • D
    $\left\langle\frac{2}{\sqrt{6}}, \frac{1}{\sqrt{6}}, \frac{1}{\sqrt{6}}\right\rangle$

Solution

Equation plane is $\frac{x}{2}+\frac{y}{2}+\frac{z}{1}=1$ $\Rightarrow x+y+2 z-2=0$ $\therefore$ direction ratio's of normal are $\langle 1,1,2\rangle$ So, Direction cosines of normal are $\left\langle\frac{1}{\sqrt{6}}, \frac{1}{\sqrt{6}}, \frac{2}{\sqrt{6}}\right\rangle$

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

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