Find the ratio in which the line joining the points (2,3,4) and (-1,4,5) is divided by the plane 3x+2y-z+2=0. Also find the point of intersection.

Let the point of intersection of the given points and the given equation be P(x,y,z). 

Let the ratio be m₁:m₂

Coordinates of P (x,y,z) ~ (  (-m₁+2m₂)/(m₁+m₂) , (4m₁+3m₂)/(m₁+m₂) ,( 5m₁+4m₂)/(m₁+m₂). Substitute values of x,y and z in equation to obtain the ratio.

ratio is : (-7/6)