Find the distance between the planes 2x-y+2z=5 and 5x-2.5y+5z=20
Answers
Answered by
5
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
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
Answered by
5
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 !!
Similar questions