ES-50 Vectors - Dot Product
The scalar or dot product of two vectors is defined as


B cos(q ) is the projection of vector B on vector A, hence, the dot product represents the product of one vector and the projection of the second vector on it.


The dot product may be shown in component form as shown.


Note: Components in like directions are multiplied. For example,given:

= 5(-3) + (-3)(2) + 2(3)
= -15 - 6 + 6 = -15 (SCALAR)
The dot product of and , ,would be...
Note: The dot product is a scalar.

Given
    
and
    
The dot product may be used to determine the angle between two vectors when the vectors are given in component form.

    
where
    
and
    
We may solve for cos ...






For example if the same data as previously is used...


The projection of a vector on a line may be obtained by the dot product of the vector and a unit vector along the line.

The angles and construction are as shown here.

Copyright ©2000 B2 Group