Two vectors are oriented at 90° to each other. What is their dot product?

If **u** and **v** are orthogonal, then
**u · v** =
|**u**| |**v**| cos 90° =
|**u**| |**v**| 0.0 = 0.0

This fact is of fundamental importance. It works for vectors of all dimensions:

The dot product of orthogonal vectors is zero. |

"Orthogonal" means "oriented at 90° to each other".
To keep things consistent, the zero vector is regarded as
orthogonal to all other vectors since
**0 · v** = 0.0
for all vectors
**v**
.

Say that two vectors **s** and **t** have a dot product that is zero.

- What can you say about the
__relative orientation__of**s**and**t**? - What can you say about the
__lengths__of**s**and**t**?