# Angle between vectors

• Dec 28th 2007, 07:58 AM
dankelly
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!!
• Dec 28th 2007, 08:03 AM
Plato
Use the arccosine function.
$\displaystyle \Theta = \arccos \left( {\frac{{A \cdot B}}{{\left\| A \right\|\left\| B \right\|}}} \right)$.
• Dec 28th 2007, 08:14 AM
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
• Dec 28th 2007, 08:28 AM
dankelly
turns out this is the way I'm supposed to do it :o..
• Dec 28th 2007, 08:30 AM
Plato
Quote:

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 $\displaystyle \left[ { - 1,1} \right]$ and its range is $\displaystyle \left[ {0,\pi } \right] \approx \left[ {0,180^ \circ } \right].$

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