Mathematics - 3D-Coordinate Geometry Question with Solution | TestHub

The equation of the plane passing through the point $(-1,-2,-1)$ and whose normal is perpendicular to both the given lines $L_1$ and $L_2$ may be written as $$\begin{array}{rlr}\Rightarrow (x+1)+7(y+2)-5(z+1)& =0& \\ & x+7y-5z+10& =0\end{array}$$ The distance of the point $(1,1,1)$ from the plane $$=\left|\frac{1+7-5+10}{\sqrt{1+49+25}}\right|=\frac{13}{\sqrt{75}}$$