Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

Direction ratios of line joining the points (1,2,-3) and (-1,-2,1) is $(-1-1,-2-2,1+3)$ i.e. (-2,-4,4) Let the direction ratios of the normal to the plane is $(a,b,c),$ then $$\begin{array}{r}2a+3b+4c=\mathrm{0....}(i)\\ -2a-4b+4c=\mathrm{0....}(ii)\end{array}$$ and By Eqs. (i) and (ii), we get $\begin{array}{rl}\frac{a}{3(4)-(4)(-4)}& =\frac{b}{(-2)(4)-(2)(4)}\\ & =\frac{c}{(2)(-4)-(-2)(3)}\\ \Rightarrow \frac{a}{12+16}& =\frac{b}{-8-8}=\frac{c}{-8+6}\\ \Rightarrow \frac{a}{28}& =\frac{b}{-16}=\frac{c}{-2}\\ \Rightarrow \frac{a}{14}& =\frac{b}{-8}=\frac{c}{-1}\end{array}$ Hence, direction ratios are (14,-8,-1)