Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

The planes are parallel. $P_1=\frac{|6-2|}{\sqrt{29}}=\frac{4}{\sqrt{29}}$. Writing the second plane as $2x-3y+4z+$ $\frac{3}{2}=0,P_2=\frac{|\frac{3}{2}-2|}{\sqrt{29}}=\frac{1}{2\sqrt{29}}.P_3=\frac{|-6-2|}{\sqrt{29}}=\frac{8}{\sqrt{29}}$. Then $P_3=16P_2,P_1=8P_2,P_1+8P_2-$ $P_3=0$ and $P_1+2P_2+3P_3=\frac{4+1+24}{\sqrt{29}}=\sqrt{29}$.