Here’s a straightforward application of arccosine, that, as far as I can tell, isn’t taught too often in Precalculus and is not part of the Common Core standards for vectors and matrices.
Find the angle between the vectors and .
Fortunately, there is the straightforward formula for the angle between two vectors and :
We recall that is the dot product (or inner product) of the two vectors and , while is the norm (or length) of the vector .
For this particular example,
In the next post, we’ll discuss why this actually works. And then we’ll consider how the same problem can be solved more directly using arctangent.