Unit Vector Between Two Points

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

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