What is the angle between #<-3,5,6> # and #<-1,9,-3>#?
Find the dot product of the vectors then divide by the magnitude of each. Finally take the cosine inverse to find
Use the definition of a dot product to find that:
The dot product is a very convenient tool that allows you to find the angle between any two vectors. It is given by:
Note: The dot product will always result in a scalar value.
With this information, the angle between the vectors <−3,5,6> and <−1,9,−3> can be found:
Step 1: Calculate the dot product
Step 2: Calculate the magnitude of each vector
Following the same procedure for
Step 3: Solve for