Question

A plane passing through the point (3, 1, 1) contains two lines whose direction ratios are 1, –2, 2 and 2, 3, –1 respectively. If this plane also passes through the point ($\alpha$, –3, 5), then $\alpha$ is equal to

(1) 5

(2) 10

(3) –5

(4) –10

Answer 1

Ans. (1) 5

Sol. Plane is a(x – 3) + b(y – 1) + c (z – 1) = 0

dr's lines are (1, –2, 2) + (2, 3, – 1) ∴ dr's of normal of plane (4, – 5, – 7)

∴ plane in 4x – 5y –7z = 0

(α, – 3, 5) lies on plane

∴ α = 5