Unit Vector Between Two Points

Posted by Jeff Schuler on Sep 20, 2009 in Uncategorized |

Suppose you are interested in finding the unit vector between two points, P and Q , which are described in cartesian coordinates as (2,-1,3) and (-1,1,0), respectively.

You would begin by finding the vector between these two points. The direction of this vector may be important so look for key words such as ``from'' P to Q . Once we have established the direction we’re going in, P to Q in this case, we subtract the beginning point from the end point. Q - P . This will give us the vector we are looking for. The next step would be to convert this vector into a unit vector, by dividing it by it’s magnitude.

These are the two formulas we are looking at:
\vec {PQ} = < (Q_x - P_x) , (Q_y - P_y) , (Q_z - P_z) >
\vec U_{PQ} = \frac{\vec {PQ}}{|\vec {PQ}|}

Note:
Here I use \vec {PQ} as my vector from P to Q and \vec U_{PQ} denotes the unit vector from P to Q .

Implementing these formulas:
\vec {PQ} = < (-1 - 2) , (1 - -1) , (0 - 3) > = < -3, 2, -3 >
\vec U_{PQ} = \frac{< -3, 2, -3 >}{|< -3, 2, -3 >|} = \frac{< -3, 2, -3 >}{\sqrt {(-3)^2 + 2^2 + (-3)^2}} = < \frac{-3}{\sqrt 22},\frac{2}{\sqrt 22},\frac{-3}{\sqrt 22}>

Hmm.. The End

If you found this page useful, consider linking to it.
Simply copy and paste the code below into your web site (Ctrl+C to copy)
It will look like this: Unit Vector Between Two Points

1 Comment

HoneyKr
Mar 31, 2012 at 9:03 am

Thanks it was really useful 😀


 

Copyright © 2017 EngineerSphere.com All rights reserved .
Sitemap