Question

The equation of the plane passing through the points (2, −1, 0) and (3, −4, 5) and parallel to the line 2x = 3y = 4z is 

(A) 125x - 90y - 79z = 340 

(B) 32x - 21y - 36z = 85 

(C) 73x + 61y - 22z = 85 

(D) 29x - 27y - 22z = 85

Answer 1

Answer is (D) 29x - 27y - 22z = 85

Given line is

2x = 3y = 4z, ⇒ x/6 = y/4 = z/3

Let the plane be ax + by + cz = 1.

We have

6a + 4b + 3c = 0

2a - b = 1

3a - 4b + 5c = 1

⇒ a = 29/35, b = 27/85, c = - 22/85

Thus, equation of plane is 29x - 27y - 22z = 85