## With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

No credit card required

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>.

16.18 ...

## With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

No credit card required