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

The plane passes through the point $(0,7,-7)$ contains the line $\frac{\mathrm{x}+1}{-3}=\frac{\mathrm{y}-3}{2}=\frac{\mathrm{z}+2}{1}$. $\therefore$ Required equation of the plane is $$\begin{array}{rl}& \left|\begin{array}{ccc}\hat{\mathrm{i}}& \hat{\mathrm{j}}& \hat{\mathrm{k}}\\ -1-0& 3-7& -2+7\\ -3& 2& 1\end{array}\right|=0\Rightarrow \left|\begin{array}{ccc}\hat{\mathrm{i}}& \hat{\mathrm{j}}& \hat{\mathrm{k}}\\ -1& -4& 5\\ -3& 2& 1\end{array}\right|=0\\ & \therefore \hat{\mathrm{i}}(-4-10)-\hat{\mathrm{j}}(-1+15)+\hat{\mathrm{k}}(-2-12)=0\end{array}$$ Hence Cartesian equation of the plane is $x+y+z=0$