# angle in => 3 dimensions must lie between 0 and pi radians?

• Mar 24th 2011, 05:20 AM
angle in => 3 dimensions must lie between 0 and pi radians?
angle in => 3 dimensions must lie between 0 and pi radians

Is this true guys? Does this means that in 3 and more dimension angle between vectors cannot be e.g., 5.4 rad? ... I hope this time someone will answer ... since this forum seems to be not very active :(
• Mar 24th 2011, 05:33 AM
Ackbeet
Quote:

Is this true guys? Does this means that in 3 and more dimension angle between vectors cannot be e.g., 5.4 rad? ...

Right, because the angle between two vectors is defined by the dot product relation

$\displaystyle \cos(\theta)=\dfrac{\mathbf{a}\cdot\mathbf{b}}{|\m athbf{a}|\,|\mathbf{a}|},$

and the arccosine function is always going to return a value in the range $\displaystyle [0,\pi].$

Quote:

I hope this time someone will answer ... since this forum seems to be not very active :(
If you're referring to the fact that your post of 4:21AM (Eastern Standard Time) today has not yet been answered, I would reply that this is an international forum, and the person best able to help you might not have logged in yet. That is, your perception of the forum not being active might be more a function of your impatience than of the actual state of affairs. It's my impression that the Trig forum is much more active than, say, Advanced Applied Math or Other Advanced Topics.

Cheers.
• Mar 24th 2011, 06:18 AM
TheChaz
(It says 8:20am CST for the OP on my browser...??)

Are we talking about spherical coordinates or vectors? Some students are so used to theta ranging from 0 - 2pi that they object to rho ranging from 0 - pi.
• Mar 24th 2011, 06:28 AM
Ackbeet
Quote:

Originally Posted by TheChaz
(It says 8:20am CST for the OP on my browser...??)