Normal Vector
Recall if a non-zero vector is orthogonal to any plane drawn in 3-space, it is also perpendicular to that plane.
In the applet below, a normal vector is seen drawn to the white plane.
The white plane is determined by the 3 blue points.
(Feel free to move these points anywhere you'd like!)
You can adjust the magnitude of the normal vector by using the slider.
Interact with this applet for a few minutes, then complete the activity that follows.
Directions:
1) Form a vector whose initial point and terminal point lie in this plane.
2) Show that this vector you've just formed is orthogonal to the normal vector.
3) Move any one (or more) of these 3 blue points around so this plane is not parallel to the xy-plane.
4) Now form another vector (different from the one you made for (1)) from any of these yellow points.
5) Show that this newly formed vector (in step 4) is also orthogonal to the normal vector.
6) Take the cross product of the vectors you constructed in steps (1) and (4).
7) Prove that the vector you formed in (6) is parallel to the normal vector.