Question

The equation of the plane containing the straight line x/2 = y/3 = z/4 and perpendicular to the plane containing the straight lines x/3 = y/4 = z/2 and x/4 = y/2 = z/3 is 

(a) x + 2y – 2z = 0

(b) 3x + 2y – 2z = 0

(c) x – 2y + z = 0

(d) 5x + 2y – 4z = 0

Answer 1

Answer is (c) x - 2y + z = 0

Let plane 1: ax + by + cz = 0 contains the line 

x/2 = y/3 = z/4

Thus, 2a + 3b + 4c = 0 ...(i)

Let plane 2: a; x + b'y + c'z = 0 is perpendicular to the plane containing the lines 

Hence, the equation of the required plane is x – 2y + z = 0