Find the coordinates of the point where the line joining the points (2,-3,1) and (3,-4,-5) cuts the plane $2 x+y+z=7$

The direction ratios of the line are $3-2,-4-(-3),-5-1$ i.e. 1,-1,-6 Hence equation of the line joining the given points is $\frac{x-2}{1}=\frac{y+3}{-1}=\frac{z-1}{-6}=r($ say $)$ Coordinates of any point on this line are $(r+2,-r-3,-6 r+1)$ If this point lies on the given plane $2 x+y+z=7$ then $2(r+2)+(-r-3)+(-6 r+1)=7 \Rightarrow r=-1$ Coordinates of any point on this line are $(-1+2,-(-1)-3,-6(-1)+1)$ i.e. (1,-2,7)