# 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 + m^{2} = 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.

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