Question

Find the angle between the given vectors to the nearest tenth of a degree.

u = <-5, 8>, v = <-4, 8>

Answer 1

@iambatman do you know how to do this one?

Answer 2

The angle between vectors stems directly from their dot multiplication, so let's take two vectors u and v and perform their dot-product.
\[(\vec u ) \times (\vec v) = \left| \left| \vec u \right| \right| . \left| \left| \vec v \right| \right|. \cos \alpha\]
Where "alpha" is the angle between these two vectors, and since it is what we are interested in finding, we solve for cos(alpha):
\[\cos \alpha= \frac{ ( \vec u) \times ( \vec w) }{ \left| \left| \vec u \right| \right|.\left| \left| \vec v \right| \right| }\]
And there we have it, the angle between two vectors is calculated by their vectorial product divided by the product of their modules, if you want, you can express the equation as:
\[\cos \alpha = \frac{ x_u x_ v + y_u y_v }{ \sqrt{x_u^2+y_u^2}\sqrt{x_v^2+y_v^2} }\]

Answer 3

costheta = u.v/||v|.||u||
=u.v=84
||v||=sq.rt 80
||u||=sq.rt 89
||v||.||u||=84.3800
costheata=84/84.3800
is this right?

Answer 4

Looks correct.
Now you have:
\[\cos \alpha=\frac{ 84 }{ 84,3800 }\]
Now you have to find the value of alpha.

Answer 5

idk how to do that

Answer 6

Well, all you have to do is apply the reciprocal operation of "cosine" by performing arc-cosine on both sides:
\[\cos \alpha=\frac{ 84 }{ 84,3800 } \iff \alpha = \cos^{-1} (\frac{ 84 }{ 84,3800 })\]

Answer 7

so will the overall answer be 5.4 degrees?

Answer 8

That's correct.