Find the point on the line (x + 2)/3 = (y + 1)/2 = (z - 3)/2

Question

Find the point on the line \(\frac{x+2}{3}=\frac{y+1}{2}=\frac{z-3}{2}\) at a distance \(3\sqrt{2}\) from the point (1, 2, 3).

Answer 1

Let \(\frac{x+2}{3}=\frac{y+1}{2}=\frac{z-3}{2} = λ\)

\(\therefore (3λ - 2, 2λ - 1, 2λ + 3)\) is any general point on the line

Now if the distance of the point from (1, 2, 3) is \(3\sqrt{2},\) then

\(\therefore\) Required point on the line is (-2, -1, 3) or \((\frac{56}{17},\frac{43}{17},\frac{77}{17})\)