Question

(i) Find the equation of the Plane passing through the points (3, -1, 2), (5, 2, 4), ( -1, -1, 6) 

(ii) Find the perpendicular distance from the point (6, 5, 9) to this plane.

Answer 1

(i) Cartesian Equation of the plane is

⇒ (x - 3)12 - (y + 1)16 + (z - 2)12 = 0

⇒ (x - 3)3 - (y + 1)4 + (z - 2)3 = 0

⇒ 3x - 4y + 3z -19 = 0

 (ii) Perpendicular distance

\(\frac{3(6)-4(5)+3(9)-19)}{\sqrt{9+16+9}}\\=\frac{18-20+27-19}{\sqrt{9+16+9}}\\=\frac{6}{\sqrt34}\)