# Can a dot product be negative in case of length?

1. Apr 12, 2014

### EmSeeSquared

Let's say A and B are 2 vectors with length in cm and the angle between them is 170°.

Obviously, the dot product of A and B will give cm2 as unit but since the value of cos(170) is negative, will the dot product be negative (something)cm2?

2. Apr 12, 2014

### Curious3141

Yes, the dot product will be negative. The geometric implication is that when A is projected onto B, the projection will be in the opposite direction to B (and vice versa).

The length merely represents the magnitude of a vector, and not its direction. A length is always non-negative, but that doesn't stop the dot product of two vectors from being negative.

Last edited: Apr 12, 2014
3. Apr 12, 2014

Aha! Thanks.