Thread: vector equation of intersection of line and plane

I have a plane that's given by the cartesian equation:

I had to write down the equation of a line passing through point and perpendicular to the plane.

so I worked it to be:

Now I have to find the point at which the line intersects the plane. I know this is going to be very simple but I simply cannot see how to do it..

After I have that I have to find the shortest distance from the point to the plane, which I should be able to do by just finding the distance between the two points considering the shortest distance is perpendicular to the plane.

Any help is greatly appreciated.
Thanks in advance.

Originally Posted by U-God

I have a plane that's given by the cartesian equation:

I had to write down the equation of a line passing through point and perpendicular to the plane.

so I worked it to be:

Now I have to find the point at which the line intersects the plane. I know this is going to be very simple but I simply cannot see how to do it..

After I have that I have to find the shortest distance from the point to the plane, which I should be able to do by just finding the distance between the two points considering the shortest distance is perpendicular to the plane.

Any help is greatly appreciated.
Thanks in advance.

Substitute the parametric equations of the line into the equation of the plane and solve for t. Then substitute that value of t back into the parametric equations of the line to get the required coordinates of the intersection point.