# Copy of Cross Product: Introduction

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).