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 the right-hand rule? |
---|---|---|---|---|---|

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

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

The cross product in 2 dimensions is not in the textbook; here is the formula for it (using the right-hand rule):

⟨Geometrically,a,b⟩ × ⟨c,d⟩ =ad−bc.

where ∠(u×v= |u| |v| sin∠(u,v),

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