If the length of the perpendicular from the point β , 0 , β , β ≠ 0 to the line, x 1 = y - 1 0 = z + 1 - 1 is 3 2 , then β is equal to

Step-by-step solution

Let Q = λ , 1 , - λ - 1 Direction ratio's of P Q ≡ λ - β , 1 - 0 ,   - λ - 1 - β ∴ P Q is perpendicular to given line, hence 1 λ - β + 0 1 - 1 - λ - 1 - β = 0 ⇒ λ - β + λ + 1 + β = 0 ⇒ λ = - 1 2 ∴     P Q =   λ - β 2 + 1 2 + - λ - 1 - β 2 = 3 2   ⇒ - 1 2 - β 2 + 1 2 + 1 2 - 1 - β 2 = 3 2 ⇒ β 2 + 1 4 + β + 1 + β 2 + 1 4 + β