Chapters

### 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.

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.

Did you like

this resource?

Bravo!

Download it in pdf format by simply entering your e-mail!

{{ downloadEmailSaved }}

## Leave a Reply