# The coordinate of the points on the line $\frac{x+2}{3} = \frac{y+1}{2} = \frac{z-3}{2}$ which are at a distance 3√2 from the point (1, 2, 3)

Q: The coordinate of the points on the line $\large \frac{x+2}{3} = \frac{y+1}{2} = \frac{z-3}{2}$ which are at a distance 3√2 from the point (1, 2, 3)

(A) (– 2, – 1, 3)

(B) (2, 2, 4)

(C) $( \frac{56}{17} , \frac{43}{17} , \frac{111}{17} )$

(D) $( \frac{47}{11} , \frac{42}{11} , \frac{56}{11} )$

Sol. Any point on the line (3λ – 2, 2λ – 1, 2λ + 3), then

(3λ – 3)2 + (2λ – 3)2 + (2λ)2 = 18

λ = 0, 13/17

points are (– 2, – 1, 3) and $( \frac{56}{17} , \frac{43}{17} , \frac{111}{17} )$

Hence (A) and (C) are the correct answers.