Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

D.R.'s can be obtained by $\begin{array}{rl}& \frac{a}{(-3)(-2)-2\times 1}=\frac{b}{1\times 1-2\times (-2)}=\frac{c}{2\times 2-2\times (-2)}\\ & \Rightarrow \frac{a}{4}=\frac{b}{5}=\frac{c}{7}\end{array}$ So, direction cosines are $$\pm \frac{4}{\sqrt{4^2+5^2+7^2}},\pm \frac{5}{\sqrt{4^2+5^2+7^2}},\pm \frac{4}{\sqrt{4^2+5^2+7^2}}$$ i.e., $\pm \frac{4}{\sqrt{90}},\pm \frac{5}{\sqrt{90}},\pm \frac{7}{\sqrt{90}}$