Orthogonal and Orthonormal Vectors
Orthogonal Vectors
Two vectors are orthogonal or perpendicular if their dot product is zero.
Example
Not perpendicular.
Orthonormal Vectors
Two vectors are orthonormal if:
1. Their dot product is zero.
2.The two vectors are unit vectors.
Examples
Calculate the value of k for the vectors 
= (1, k) and 
= (−4, k) knowing that they are orthogonal.
· = 0 −4 + m2 = 0; m = ± 2
If { , } is an orthonormal basis, calculate:
1 · = 1 · 1 · cos 0° = 1
2 · = 1 · 1 · cos 90° = 0
3 · = 1 · 1 · cos 90° = 0
4 · = 1 · 1 · cos 0° = 1
If {, } is an orthonormal basis and 
are:
Calculate the value of k knowing that 
.
If {, } is an orthonormal basis and are:
Calculate the value of k for the two orthogonal vectors.
