# Selftest: Cross product

From Robotics

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Exercises for chapter Vector algebra | Article: Cross product |
Next exercise: Introduction to vector algebra → |

1. **Please mark the right transforms:**

→ | The magnitude of the cross product results from the following equation: . In this case the angle is 90° and so the magnitude is |ab|. | ||||||||||||

→ | The magnitude of the cross product results from the following equation: . Here the angle is 180° and the related sine is zero. So the result is 0. |

2. **Please mark the right transforms: (x,y,z are coordinate axes, a and b are arbitrary)**

The cross product is commutative. | |||||||||||||

→ | The first answer implies that the cross product is not commutative. This can easily be proved by the right-hand-rule. Further information: see Cross product |

3. **Please solve the following exercise:**

→ To compute the cross product the component representation is used. |

4. **Please solve the following exercise:**

→ To compute the cross product the component representation is used. |

5. **Please solve the following exercise:**

→ To compute the cross product the component representation is used. |

6. **The following vectors are given.**

Please mark the correct statements sonsidering the the given vectors.

The vector is perpendicular to the plane that is spanned by the vectors and . | |

The magnitude of the cross product equals the area of the parallelogram that is spanned by the vectors and . | |

The vectors , and form a rectangular coordinate system. So they are arranged as thumb, middle finger and forefinger of the right hand. |