Practicing Success
The distance of the point (3, –2, 1) from the plane 2x – y + 2z + 3 = 0 is : |
\(\frac{3}{13}\) \(\frac{13}{3}\) \(\frac{14}{3}\) \(\frac{3}{14}\) |
\(\frac{13}{3}\) |
Distance of point (x, y, z) from plane Ax + By + Cz = D is $|\frac{Ax_1 + By_1 + Cz_1 = D}{\sqrt{A^2+B^2}}|$ ....(i) given points is (3, -2, 1) x1 = 3, y1 = -2, z1 = 1 & equation of plane is 2x - y + 2z + 3 = 0 2x - y + 2z = -3 -(2x - y + 2z) = 3 ⇒ -2x+ y - 2z = 3 comparing with Ax + By + Cz = D A = -2, B = 1, C = -2, D = 3 Distance of point form the plane = $|\frac{(-2×3)+(1×-2)+(-2×1)-3}{\sqrt{(-2)^2+(1)^2+(2)^2}}|$ $=|\frac{(-6)+(-2)+(-2)-3}{\sqrt{4+1+4}}|⇒|\frac{-13}{\sqrt{9}}|$ $=|\frac{-13}{3}|=\frac{13}{3}$ Option 2 is correct. |