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

The vector along the required plane is $\left|\begin{array}{ccc}\hat{\mathrm{i}}& \hat{\mathrm{j}}& \hat{\mathrm{k}}\\ 3& 4& 2\\ 4& 2& 3\end{array}\right|=8\hat{\mathrm{i}}-\hat{\mathrm{j}}-10\hat{\mathrm{k}}$.

Thus, the normal vector ($\overrightarrow{\mathrm{n}}$) to the plane is $\left|\begin{array}{ccc}\hat{\mathrm{i}}& \hat{\mathrm{j}}& \hat{\mathrm{k}}\\ 8& -1& -10\\ 2& 3& 4\end{array}\right|=26\hat{\mathrm{i}}-52\hat{\mathrm{j}}+26\hat{\mathrm{k}}$..