# B How to specify direction in 3 dimensional world

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1. Apr 7, 2017

### donaldparida

I have just started studying vector algebra and i was wondering how is the direction of a vector (or any point object) specified in 3 dimensions. I know how to indicate the direction of a vector in 1 dimension and 2 dimensions. Is the direction of a vector in 3 dimensions stated by using angles or is there any other way to do so?

2. Apr 7, 2017

### A.T.

By the vector itself?

You can represent a vector in polar coordinates, which include angles.

Last edited: Apr 7, 2017
3. Apr 7, 2017

### vanhees71

A direction is given by a unit vector. Each unit vector can be specified by spherical coordinates, i.e., two angles. You know this from latitudes and longitudes on Earth. In physics one uses a slightly adapted version of this, which is as follows: Take a Cartesian coordinate system and specify its $z$ axis as the polar axis. Then the unit vector is given in terms of the polar angle $\vartheta \in [0,\pi]$ and azimuthal angle $\varphi \in [0,2 \pi[$ as
$$x=\cos \varphi \sin \vartheta, \quad y=\sin \varphi \sin \vartheta, \quad z=\cos \vartheta.$$
To visualize this, see the following figure from Wikipedia

https://en.wikipedia.org/wiki/File:3D_Spherical.svg

For the unit vector you have of course $r=1$.