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
.
This problem is equivalent to finding the angle between the lines
and
. The angle
is not drawn in standard position, which makes measurement of the angle initial daunting.
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.