The distance of the point (1, 1, 9) from the point of intersection of the line  x−31=y−42=z+52 and the plane x+y+z=17 is:

The given line is x−31=y−42=z−52=λThe general point on the line is ⇒x=λ+3,y=2λ+4,z=2λ+5This point also lies on the plane hence, ⇒λ+3+2λ+4+2λ+5=17⇒λ=1The point of intersection is Q4,6,7Hence, the distance PQ=9+25+4=38