# Cross Product: Introduction

- Author:
- 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).