The coordinates of a point on the line x−12=y+1−3=z at a distance 414 from the point (1,−1,0) are

Let for required point x−12=y+1−3=z=λ⇒(1+2λ,−1−3λ,λ) Now distance between this point with (1,−1,0) is 414⇒(2λ)2+(−3λ)2+λ2=16×1414λ2=16×14λ=±4⇒(9,−13,4) and (−7,11,−4) Ans.