1. Intersection between - Lines, - Planes and - a plane & a Line

2. Intersection between Lines
Example-1:
Show that the following lines intersect and find their point of intersection.

3. Intersection of a Line and a Plane
Example-2: Find the point at which the line with parametric equations x = 2+3t, y = -4t and z = 5+t intersects the plane 4x+5y-2z = 18.

4. Intersection between Planes
Example-3:
Show that the following planes intersect and find their line of intersection.

5. Distance between Points, Lines and Planes

6. Distance between a Point and a Plane
Find a formula for the distance D from the point p1(x1, y1,z1) to the plane ax+by+cz+d=0.

7. Example-4:
Find the distance between the point Q(1, 5, -4) and the plane 3x-y+2z = 6.

8. Distance between a point and a line in space

9. Example-5: x = -2+3t y = -2t z = 1+4t
Find the distance between the point Q(3, -1, 4) and the line given by
x = -2+3t
y = -2t
z = 1+4t

10. Distance between parallel planes
Example-6: Find the distance between the following two parallel planes: 3x-y+2y = 6 6x-2y+4z = -4