MCV4U1- UNIT SEVEN-LESSON THREE UNIT SEVEN - LESSON THREE: DOT PRODUCT There are two ways that we can multiply vectors. The DOT PRODUCT is one of these ways. Note that when we DOT two vectors, we end up with a SCALAR. GEOMETRIC FORM OF DOT PRODUCT: For two non-zero vectors a and b , a b a b cos , 0 180 Ex. 1. Find u v for each of the following. a) u 7, v 12, 60 b) u is a unit vector, v 8, 5 4 ALGEBRAIC FORM OF DOT PRODUCT IN TWO DIMENSIONS: a a1 , a 2 b b1 , b2 a b a1b1 a 2 b2 ALGEBRAIC FORM OF DOT PRODUCT IN THREE DIMENSIONS: a a1 , a 2 , a3 b b1 , b2 , b3 a b a1b1 a 2 b2 a3 b3 1 MCV4U1- UNIT SEVEN-LESSON THREE Ex. 2. Find u v for each of the following. a) u 5,3, v 6,4 b) u 6i 2 j 5k , v i 3 j 2k Ex. 3. Find the angle between the vectors a 5,7 and b 2,4 . Properties of DOT PRODUCT: a b b a commutative 2 aa a ka b a kb k a b ; k a b c a b a c distributi ve across addition or subtraction 1. a b 0 iff a b 2. 3. 4. 5. 2