## Products of Vectors

2.4 Products of Vectors

### Learning Objectives

By the end of this section, you will be able to:

- Explain the difference between the scalar product and the vector product of two vectors.
- Determine the scalar product of two vectors.
- Determine the vector product of two vectors.
- Describe how the products of vectors are used in physics.

### Scalar Product (or the Dot Product)

**Practice!**

Practice 2.4.1 |
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What is the dot product ? |

(a) (120 m^{2})cos 78.0° |

(b) (120 m^{2})sin 78.0° |

(c) (120 m^{2})cos 62.0° |

(d) (120 m^{2})sin 62.0° |

(e) Something else |

**Discuss!**

Consider how you would answer this question. Then bring this to class for a group discussion.

Based on the vectors in the diagram above, find the following scalar (dot) products:

### Vector Product (or the Cross Product)

**Practice!**

Practice 2.4.2 |
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What is the cross product ? |

(a) (96.0 m^{2}) sin 25.0° |

(b) (96.0 m^{2}) cos 25.0° |

(c) -(96.0 m^{2}) sin 25.0° |

(d) -(96.0 m^{2}) cos 25.0° |

(e) Something else |

**Discuss!**

Consider how you would answer this question. Then bring this to class for a group discussion.

Based on the vectors in the diagram above, find the following scalar (dot) products: