1. Objective: Projection of vector onto another. Orthogonal vectors.
Warm up
Find the angle between the two vectors:
The angle between vectors v and w is Find
Orthogonal (vectors):
Vectors v and w are orthogonal iff

2. Example 1 Determine whether v and w are orthogonal. a. b.

3. Projection of a vector onto another.
Pushing boat down the ramp
Pressing the boat against ramp
(due to gravity) pulling straight down
A method of finding and involves projecting a vector onto another.

4. Projection of v onto w: v w

5. Example 2
Find the vector projection of onto
Write v as the sum of two orthogonal vectors.

6. Example 3
Let and
Find
Write v as the sum of two orthogonal vectors.