How to specify direction in 3 dimensional world

  • #1
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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?
 

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  • #2
A.T.
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how is the direction of a vector (or any point object) specified in 3 dimensions.
By the vector itself?

Is the direction of a vector in 3 dimensions stated by using angles or is there any other way to do so?
You can represent a vector in polar coordinates, which include angles.
 
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  • #3
vanhees71
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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##.
 

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