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The Distance Formula in 3 Dimensions

You know that the distance A B between two points in a plane with Cartesian coordinates A ( x 1 , y 1 ) and B ( x 2 , y 2 ) is given by the following formula:

A B = ( x 2 x 1 ) 2 + ( y 2 y 1 ) 2

In three-dimensional Cartesian space, points have three coordinates each. To find the distance between A ( x 1 , y 1 , z 1 ) and B ( x 2 , y 2 , z 2 ) , use the formula:

A B = ( x 2 x 1 ) 2 + ( y 2 y 1 ) 2 + ( z 2 z 1 ) 2

 

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