Let image of point (8, 5, 7) with respect to line x-1 / 2 = y+1 / 2 = z-2 / 5 is

Question

Let image of point (8, 5, 7) with respect to line \(\frac {x-1}{2} = \frac {y+1}{2} = \frac {z-2}{5}\) is \((\alpha , \beta , \gamma).\)Then \(\alpha + \beta + \gamma\) is equal to 

(1) 10 

(2) 12 

(3) 9 

(4) 14

Answer 1

Correct option is (4) 14

Given point (8, 5, 7)

Let Q be general point.

(x, y, z) = (2λ + 1, 3λ – 1, 5λ + 2) 

∴ Now D.R. of P.Q 

PQ ⇒ (2λ + 1 – 8, 3λ – 1 – 5, 5λ + 2 – 7) 

= (2λ – 7, 3λ – 6, 5λ – 5) ...(1) 

∴ D.R. of line ....(2) 

From (1) and (2) 

2(2λ – 7) + 3(3λ – 6) + 5(5λ – 5) = 0 

4λ – 14 + 9λ – 18 + 25λ – 25 = 0 

38λ – 57 = 0