Answer: the required equation is 5x - 6y + 5z = 7
Step-by-step explanation:
Given that;
points : (-1, 1, -5) and (4, -5, 0).
mid point : ( [(-1+4)/2], [(1-5)/2], [(-5+0)/2]
⇒ midpoint : ( 3/2, -2, -5/2 )
x₀ y₀ z₀
Direction vector n = [4-(-1)], [ -5 - 1], [ 0 - (-5)]
⇒ Direction vector n = < 5, -6, 5 >
General equation plane : n(x-x₀, y-y₀, z-z₀) = 0
so we substitute
⇒ (5, -6, 5) (x-3/2, y-(-2), z-(-5/2) ) = 0
⇒ (5, -6, 5) (x - 3/2, y + 2, z + 5/2) ) = 0
⇒ 5(x - 3/2) - 6(y + 2 ) + 5(z + 5/2) = 0
⇒ 5x - 15/2 - 6y - 12 + 5z + 25/2 = 0
⇒ 5x - 6y + 5z = 15/2 + 12 - 25/2
⇒ 5x - 6y + 5z = 7
Therefore, the required equation is 5x - 6y + 5z = 7
