The direction cosines of the line, which is perpendicular to the lines with direction rations $-1,2,2$ and…

The direction cosines of the line, which is perpendicular to the lines with direction rations $-1,2,2$ and $0,2,1$, are respectively
  1. $\frac{1}{3}, \frac{-2}{3}, \frac{-2}{3}$
  2. $\frac{2}{3}, \frac{-1}{3}, \frac{2}{3}$
  3. $\frac{-1}{3}, \frac{2}{3}, \frac{2}{3}$
  4. $\frac{1}{3}, \frac{2}{3}, \frac{2}{3}$

Solution

The d.r.s can be obtained by $\begin{aligned} & \frac{a}{2 \times 1-2 \times 2}=\frac{b}{0 \times 2-(-1) \times 1}=\frac{c}{(-1) \times 2-0 \times 2} \\ & \Rightarrow < 2,-1,2> \\ & \Rightarrow \text { d.c's are } < \frac{2}{3}, \frac{-1}{3}, \frac{2}{3}> \end{aligned}$

Asked in: MHT CET 2022 (11 Aug Shift 1)

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