Question

Find the equation of the plane mid - parallel to the planes 2x – 3y + 6z + 21 = 0 and 2x – 3y + 6z – 14 = 0

Answer 1

Formula : The equation of mid parallel plane is , say 

Plane 1:ax + by + cz + d1 = 0 & 

Plane 2:ax + by + cz + d2 = 0 is given by the formula

Mid parallel plane = ax + by + cy + \(\frac{(d_1+d_2)}2\) = 0

where (d₁,d₂) are constants of the planes 

Therefore , 

First Plane 2x – 3y + 6z + 21 = 0 …… (1) 

Second plane 2x – 3y + 6z – 14 = 0 …… (2) 

Using equation (1) and (2)

Mid parallel plane = 2x - 3y + 6x + \(\frac{21-14}2\) = 0

4x – 6y + 12z + 7 = 0