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Copy of Cross Product: Introduction

Autor:ashum, Tim Brzezinski
The cross product of any 2 vectors u and v is yet ANOTHER VECTOR! In the applet below, vectors u and v are drawn with the same initial point. The CROSS PRODUCT of u and v is also shown (in brown) and is drawn with the same initial point as the other two. Interact with this applet for a few minutes by moving the initial point and terminal points of both vectors around. Then, answer the questions that follow.

1.

Use GeoGebra to measure the angle at which the line containing u intersects the line containing the cross product vector. What do you get?

2.

Use GeoGebra to measure the angle at which the line containing v intersects the line containing the cross product vector. What do you get?

3.

Given your responses for (1) and (2) above, what can we conclude about the cross product of any two vectors with respect to both individual vectors themselves?

4.

Is it possible to position vectors u and v so that their cross product = the zero vector? If so, how would these 2 vectors be positioned?

5.

How would vectors u and v have to be positioned in order for their cross product to have the greatest magnitude? Use GeoGebra to help informally support your conclusion(s).

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