A line through (1,-1,2) with direction ratios 3,2,2 meets the plane x+2 y+3 z=18 . What is the point of intersection of line and plane?

Step-by-step solution

Let the line p(1,-1,2) and meet the plane at point Q. Direction ratios of the line from the point (1, -1, 2) to the given plane is 3,2,2 x-1 3 = y+1 2 = z-2 2 = Co-ordinates any points on the line PQ are aligned & x=3 +1, y=2 -1, z=2 +2 & x+2 y+3 z=18 & 3 +1+4 -2+6 +6=18 & 13 +5=18 & 13 =13 & aligned Hence, the co-ordinates of Q are (3+1,2-1,2+2)=(4,1,4)