Question

Help Please :)
Find the angle between the given vectors to the nearest tenth of a degree.

u = <6, -1>, v = <7, -4>

Answer 1

Then what?

Answer 2

Note there is more than one way of solving for angle theta between the two geometric vectors but the way I will use is that we will find find the angle vector \(\bf \vec v\) makes with the x-axis and then subtract the angle \(\bf \vec u\) makes with the x-axis and that will get you \(\bf \theta\)

Answer 3

So I will first find the angle 'v' makes with the x-axis, then the angle 'u' makes with the x-axis and then subtract the two. Let's call the angle v makes \(\bf \alpha\) and the angle that u makes \(\bf \beta\). Let's find \(\bf \alpha\) first using our trig ratios:

Answer 4

ok

Answer 5

Hence \(\bf \alpha\) is:\[\bf \alpha = \arctan(4/7) \approx 29.7 \ degrees\]Now to solve for \(\bf \beta\):Hence \(\bf \beta\) is:\[\bf \beta = \arctan(1/6) \approx 9.5 \ degrees\]