If the angle between the line x = (y - 1)/2 = (z - 3)/λ and the plane x + 2y + 3z = 4 is cos^{-1}(5/14) then λ is equal to

- 3/2
- 2/5
- 2/3
- 5/3

**Answer**

(x - 0)/1 = (y - 1)/2 = (z - 3)/λ

x + 2y + 3z = 4

Angle between the line and plane is

cos(90 - θ) = (a_{1}a_{2} + b_{1}b_{2} + c_{1}c_{2}) / √(a_{1}^{2} + b_{1}^{2} + c_{1}^{2})√(a_{2}^{2} + b_{2}^{2} + c_{2}^{2})

sinθ = 1 + 4 +3λ / √14 x √(5 + λ^{2}) = 5 + 3λ / √14 x √(5 + λ^{2})

But given that angle between line and plane is

θ = cos^{-1}(5/√14) = sin^{-1}(3/√14)

sinθ = 3/√14

3/√14 = 5 + 3λ / √14 x √(5 + λ^{2}))

**The correct option is C.**