Let any point on the intersecting line
===λ (say)
is
(−3λ−1,2λ+3,−λ+2) Since, the above point lies on a line which passes through the point (-4,3,1)
Then, direction ratio of the required line
=<−3λ−1+4,2λ+3−3, −λ+2−1> or
<−3λ+3,2λ,−λ +1> Since, line is parallel to the plane
x+2y−z−5=0 Then, perpendicular vector to the line is
+2− Now
(−3λ+3)(1)+(2λ)(2) +(−λ+1)(−1)=0 ⇒λ=−1 Now direction ratio of the required line
=<6,−2,2> or
<3, −1,1> Hence required equation of the line is
==