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:
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For two non-zero vectors a and b , a  b  a b cos  ,
0    180
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Ex. 1. Find u  v for each of the following.
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a) u  7, v  12,   60
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b) u is a unit vector, v  8,  
5
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ALGEBRAIC FORM OF DOT PRODUCT IN TWO DIMENSIONS:
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a  a1 , a 2 
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b  b1 , b2 
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a  b  a1b1  a 2 b2
ALGEBRAIC FORM OF DOT PRODUCT IN THREE DIMENSIONS:
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a  a1 , a 2 , a3 
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b  b1 , b2 , b3 
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a  b  a1b1  a 2 b2  a3 b3
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MCV4U1- UNIT SEVEN-LESSON THREE
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Ex. 2. Find u  v for each of the following.
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a) u   5,3, v  6,4
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b) u  6i  2 j  5k , v  i  3 j  2k
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Ex. 3. Find the angle between the vectors a  5,7  and b  2,4 .
Properties of DOT PRODUCT:
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a  b  b  a commutative 
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aa  a
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ka  b  a  kb  k a  b ; k  
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a  b  c  a  b  a  c distributi ve across addition or subtraction 
1. a  b  0 iff a  b
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