Add: | Scalar | Point | Vector | Subtract: | Scalar | Point | Vector | Multiply: | Scalar | Point | Vector | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Scalar | Scalar | ― | ― | Scalar | ― | ― | Scalar | ― | Vector | |||

Point | ― | ― | Point | ― | Vector | Point | ― | ― | ― | |||

Vector | ― | Point | Vector | ― | ― | Vector | Vector | ― | Depends |

Name | Symbol | Result | Order matters? | Depends on lengths? | Depends on right-hand rule? |
---|---|---|---|---|---|

Dot product | ⋅ | Scalar | No | Yes | No |

Cross product | × | Scalar in 2D, vector in 3D |
Yes | Yes | Yes |

Tensor product | ⊗ | Dyad | Yes | No | No |

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