Two vectors are given by a = 3.3 x - 6.4 y and b = -17.8 x + 5.1 y. What is the angle between vector b and the positive x-axis?
Here's a more rigorous way to do this (easier way at the bottom):
We're asked to find the angle between vector
We'll imagine there is a vector that points in the positive
The dot product of these two vectors is given by
#b#is the magnitude of #vecb#
#i#is the magnitude of #veci#
#phi#is the angle between the vectors, which is what we're trying to find.
We can rearrange this equation to solve for the angle,
We therefore need to find the dot product and the magnitudes of both vectors.
The dot product is
The magnitude of each vector is
Thus, the angle between the vectors is
Here's an easier way to do this:
This method can be used since we're asked to find the angle between a vector and the positive
Therefore, we can simply take the inverse tangent of vector
We must add