# Thread: Angle between vectors

1. ## Angle between vectors

I can do the full equation but the problem is trying to find the angle between two vectors,

So if I had the problem

Find angle between these two given vectors:
A = (2,1,-3)
B = (1,-1,1)

A.B = -2

|a| = sqrt14
|b| = sqrt3

so

-2/sqrt42 = -0.309

I know cos(thetre) = A . B / a b

but I'm still not sure how to go about finding the angle
how do I work out the angle?? Iam quite new to vectors so Iam guessing this is quite obvious,
Please can someone point it out for me!!
I have the answer 108 degrees in my notes I just dont know how to get that!!

2. Use the arccosine function.
$\Theta = \arccos \left( {\frac{{A \cdot B}}{{\left\| A \right\|\left\| B \right\|}}} \right)$.

3. Thanks, is that the only way to solve this type of question? Its no big deal I just I cant see arccos written in my notes

4. turns out this is the way I'm supposed to do it ..

5. Originally Posted by dankelly
Thanks, is that the only way to solve this type of question? Its no big deal I just I cant see arccos written in my notes
I find that really odd if true.
The arccosine function is one of the most useful in the study of vectors.
Its domain is $\left[ { - 1,1} \right]$ and its range is $\left[ {0,\pi } \right] \approx \left[ {0,180^ \circ } \right].$

Even a minimal scientific calculator will have a preprogrammed button for the arccosine. It may be signed as $\cos ^{ - 1}$.