 
Summary: 12.3 Dot Product
Multiplication of Vectors
There are two types of multiplication of vectors.
· Dot Product: The multiplication of two vectors produces a scalar
· Cross Product: The multiplication of two vectors produces a vector
Dot product
Properties of dot product
Question 8/812: Find a ifb 4 3a j k=  and b i2 4 6j k= + + .
Given two vectors 1 2 3, ,u u ,u u= 1 2 3, ,v v v v= .
Their dot product is
1 1 2 2 3 3u v u v u v u v + += (*) Result is a scalar
Similar definition for
vectors in 2space
If u ,v and w are vector and is a
scalar. Then
k
1. u v v u =
2. ( )u v w u v u w + = +
3. ( ) ( ) (k u v ku v u kv) = =
4. 2
