1. Find the intersection point of the line (x-1)/2=(y+1)/3=z-2 and the plane 2x+y-z=17.
2. Find the distance from point Q(1,-2,3) to the plane 2x-y-z=6.
Need steps and solutions.....Thanks!
1. Let's first parameterize the line so t=(x-1)/2=(y+1)/3=z-2, so then a point on the line is
u = (2t+1,3t-1,t+2) and if the equation of the plane is 2x+y-z=17 then their intersection occurs when
2(2t+1)+(3t-1)-(t+2)=17 that is t=3, substituting this back into the general form of the line we ...
This shows how to find an intersection of a line and plane and the distance from a point to a plane.