Question

If the plane P passes through the intersection of two mutually perpendicular planes 2 x + ky – 5 z = 1 and 3 kx – ky + z = 5, k < 3 and intercepts a unit length on positive x -axis, then the intercept made by the plane P on the y -axis is

• A. $\frac{1}{11}$
• B. $\frac{5}{11}$
• C. 6
• D. 7

Answer 1

Answer: (D)

7

Answer 2

The correct answer is (D):
P1: 2x+ky-5z = 1
P 2 : 3 kx – ky + z = 5
∵ P1⊥P2 ⇒ 6k-k2+5 = 0
⇒ k = 1,5
∵ k<3
∴ k = 1
P1 : 2x+y-5z = 1
P2 : (2x+y-5z-1)+λ(3x-y+z-5) = 0
Positive x-axis intercept = 1
$⇒ \frac{1+5λ}{2+3λ} = 1$
⇒ λ = $\frac{1}{2}$
∵ P : 7x+y-4z = 7
y intercept = 7.