If #A = <3 ,8 ,-1 >#, #B = <4 ,-3 ,-1 ># and #C=A-B#, what is the angle between A and C?
We can find the angle between vectors using the Dot Product
The dot product states that for vectors a and b:
The dot product is sometimes called the inner product, because of the way the vectors a and b are multiplied and summed.
In algebra we are used to multiplying brackets in the following way.
In the case of the dot product we multiply the vectors in the following way.
So we are just multiplying corresponding components and then adding them together.
Now to our example:
First find the product of:
Now find the magnitudes of A and C:
So we have for:
( 2 .d.p.)
So the angle between vectors A and C is
Notice from the diagram that the angle found by the dot product, is the angle between the vectors where they are pointing in the same relative direction.