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.
Loved reading this thankss