The direction cosines of the line which is perpendicular to the lines with direction cosines proportional to $\langle 1,-2,-2\rangle$ and $\langle 0,2,1\rangle$ is given by

Question

Aicharya · Accepted Answer

Let $l, m, n$ be the direction cosines of the required line. Since, it is perpendicular to the lines whose direction cosines are proportional to $1,-2,-2$ and $0,2,1$ respectively Thus, $l-2 m-2 n=0$ and $2 m+n=0$ On solving $\frac{1}{2}=\frac{m}{-1}=\frac{n}{2}$ Thus, DR's of required line are proportional to $(2,-1,2)$ Hence, direction cosines are $=\left(\frac{2}{3},-\frac{1}{3}, \frac{2}{3}\right)$

The direction cosines of the line which is perpendicular to the lines with direction cosines proportional to…

Solution