Question

How exactly do I solve this?

Find the perpendicular distance between the planes, 2x + 2y + z = 6 and 2x + 2y + z = 10​

Answer 1

1 1/3 (or 1.33333..)

Explanation:

d: distance A₁x+B₁y+C₁z+D₁=0 2x+2y+z-6=0 ... D₁ = -6

A₂x+B₂y+C₂z+D₂=0 ... A₂=2 B₂=2 C₂=1 D₂= -10

d = |D₂ - D₁| / (√A₂² + B₂² + C₂²)

= |-10 - -6| / (√2² + 2² + 1²)

= |-4| / √9

= 4/3

= 1 1/3