Measuring Angles Between Vectors
The dot product in disguise
16.17 Identify the alternate dot product formula, which expresses a dot product in terms of the magnitude of the vectors.
According to Problem 16.1, given vectors v = <a, b> and w = <c, d>, the dot product is defined according to the following formula.
v · w = ac + bd
You can also calculate the dot product according to an alternate formula, which is based on the magnitudes of the vectors and the cosine of the angle θ between those vectors.
The alternate version is handy when you don’t know the components of the vectors.
Note: In Problems 16.18–16.21, v = <0, 5> and w = <2, 2>.