1. Assigned work: pg.377 #5,6ef,7ef,8,9,11,12,15,16 Pg. 385#2,3,6cd,8,9-15 So far we have : Multiplied vectors by a scalar Added vectors Today we will: Multiply vectors in a way to produce a scalar This is called a Dot Product S. Evans

2. 7.3/7.4 Dot Product of Two Vectors Dot Product (also called Scalar Product or Inner Product) If are two vectors and is the angle between them, then the dot product of is: Note: The result is a scalar (no direction) S. Evans

3. 7.3/7.4 Dot Product of Two Vectors Properties of Dot Product: Commutative Distributive Magnitudes Associative with a scalar k S. Evans

4. 7.3/7.4 Dot Product of Two Vectors Ex 1: Given and the angle between is determine: a) b) S. Evans

5. 7.3/7.4 Dot Product of Two Vectors S. Evans The sign of the dot product depends on the sign of

6. 7.3/7.4 Dot Product of Two Vectors A common use of dot product is to test if two vectors are perpendicular………. Two vectors are perpendicular IFF: S. Evans

7. 7.3/7.4 Dot Product of Two Vectors Dot Product in Component (Algebraic) Form: In R 2 : If In R 3 : If Read section 7.4 to see proof S. Evans

8. 7.3/7.4 Dot Product of Two Vectors Ex 2: If Calculate: S. Evans

9. 7.3/7.4 Dot Product of Two Vectors Ex 3: For what value of k are the vectors perpendicular? S. Evans

10. 7.3/7.4 Dot Product of Two Vectors Ex 4: Find the angle between S. Evans

11. 7.3/7.4 Dot Product of Two Vectors Ex 5: The parallelogram OACB has one vertex,O, at the origin and two non-parallel sides defined by Calculate the angle between the diagonals. S. Evans