QUESTION 5:
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?
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.