I have performed numerous calculations of dot products throughout my math courses, but I think I lack a fundamental understanding of what it actually means, beyond the abstract way I have been taught to deal with them. I know the definitions (it's the inner product, or the projection of A on to B), but the answer you get with a dot product, does it have a geometric representation? What specifically does it mean?(adsbygoogle = window.adsbygoogle || []).push({});

For example, if you have two vectors (1,4) and (5,0), the dot product is 5. But what does that 5 really mean and can you represent it geometrically. I know it is a scalar and not a vector, but I am hoping there is a way to represent it. Obviously, if you had (2,4) and (5,0) instead, the dot would be twice as large because the angle between them is less and the vectors "share" more in common (a larger first component).

So what I am asking is if there is any true meaning to these dot product numbers of 5 and 10 and is there a way to geometrically represent them? Or, are they merely numbers for calculating the angle in between vectors, where a larger dot product means a smaller angle.

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Confused about the True Geometric Meaning of a Dot Product Answer.

Loading...

Similar Threads - Confused True Geometric | Date |
---|---|

A Modular forms, dimension and basis confusion, weight mod 1 | Nov 23, 2016 |

I True False Question | Apr 3, 2016 |

I Confused about basis vector notation | Mar 29, 2016 |

I Confused on definition of projection | Mar 12, 2016 |

Confusion about eigenvalues of an operator | Feb 21, 2016 |

**Physics Forums - The Fusion of Science and Community**