Question

Find the distance between the planes 2x-y+2z=5 and 5x-2.5y+5z=20

Answer 1

given equation of two planes , 

2x - y + 2z = 5 

5x -2.5y + 5z =20 

divide both sides by 2.5 in 2nd equation, 
5/2.5x -2.5y/2.5 +5z/2.5 = 20/2.5 

2x - y + 2z = 8 

now, you can see that both planes are parellel . 

distance between two parallel planes = |8 -5|/√(2² +1² +2²) 

= 3/3 = 1 unit

Answer 2

Hey !!

Step-by-step explanation:

P₁ = 2x - y + 2x = 5

P₂ = ₂x - 2.5y + 5z = 20

        => 2x - y + 2z = 20 / 2.5

= 20 / 5 × 2

= 8

Distance = | d₂ - d₁ / √a² + b² + c² |

    = | 8 - 5 / √(2)² + (-1)² + (2)² |

     = | 3 / √4 + 1 + 4 |

     = | 3 / √9 |

     = 3 / 3

      = 1 unit.

Good day !!