Lesson 6.4 – Dot Products

1. Lesson 6.4 – Dot Products The dot product of two vectors is given by The result is a scalar (number) – not a vector

2. The dot product has all the properties of multiplication

3. Answer Example: Find the dot product 13 • FYI… • Mechanical work is the dot product of force and displacement vectors. • Magnetic flux is the dot product of the magnetic field and the area vectors

4. u v Angle Between 2 Vectors You could find the angle between the vectors using a 2 step process: Find the direction angle of u Find the direction angle of v Find the difference Or with 1 step: This is a dot product since u and v are vectors

5. Answer Example Find the angle between the vectors 104.6

6. Orthogonal Vectors All vectors can be written as the sum of 2 perpendicular vectors: u w2 w1 Perpendicular vectors are also called orthogonal, and their dot product = 0

7. F v 30o Orthogonal Vectors can be used to find the projection of a vector onto another Projection: The force and direction of a vector that balances (equals) another vector The projection of u onto v is: What vector, v, is needed to keep the wagon from rolling back if F is 300 pounds? F = -300j v = cos 30oi + sin 30oj