[color=#000000]Recall if a non-zero vector is orthogonal to any plane drawn in 3-space, it is also perpendicular to that plane. [br][br]In the applet below, a [/color][b][color=#980000]normal vector[/color][/b][color=#000000] is seen drawn to the [/color][b]white plane[color=#1e84cc]. [/color][/b][color=#000000][br]The [/color][b]white plane[/b][color=#000000] is determined by the [/color][color=#0000ff][b]3 blue points.[/b][br][/color][color=#000000](Feel free to move [/color][color=#0000ff][b]these points[/b] [/color]anywhere you'd like!)[br]You can adjust the [b][color=#980000]magnitude[/color][/b] of the [b][color=#980000]normal vector[/color][/b] by using the [b][color=#980000]slider. [/color] [/b][br][br]Interact with this applet for a few minutes, then complete the activity that follows.

[b][color=#0000ff]Directions:[br][br][/color][/b][color=#000000]1) Form a vector whose initial point and terminal point lie in this plane.[br][br][/color][color=#000000]2) Show that this vector you've just formed is orthogonal to the normal vector.[br][/color][br]3) Move any one (or more) of these [b][color=#0000ff]3 blue points[/color][/b] around [b]so this plane is not parallel to the xy-plane.[/b][br][br]4) Now form another vector (different from the one you made for (1)) from any of these yellow points.[br][color=#000000][br]5) Show that this newly formed vector (in step 4) is also orthogonal to the normal vector.[br][br][/color][color=#000000]6) Take the cross product of the vectors you constructed in steps (1) and (4).[br][br]7) Prove that the vector you formed in (6) is parallel to the normal vector. [/color]