Distance between (1,2,3) and (4,5,6)

Enter point 1

(x1: , y1: z1: )

Enter point 2

(x2: y2: z2: )
  

Calculate the distance between:

(1, 2, 3) and (4, 5, 6)

Also calculate the parametric and symmetric forms

Distance formula for 3-D points

Distance = √(x2 - x1)2 + (y2 - y1)2 + (z2 - z1)2

Distance = √(4 - 1)2 + (5 - 2)2 + (6 - 3)2

Distance = √32 + 32 + 32

Distance = √9 + 9 + 9

Distance = √27

Distance = 5.1961524227066

Parametric Equation Form:

(x,y,z) = (x0,y0,z0) + t(a,b,c)

Plugging in our numbers, we get:

(x,y,z) = (1,2,3) + t(4 - 1,5 - 2,6 - 3)

(x,y,z) = (1,2,3) + t(3,3 ,3)

x = 1 + 3t

y = 2 + 3t

z = 3 + 3t

Symmetric Equation Form:

x - x0
a
=
  
y - y0
b
=
  
z - z0
c

Plugging in our numbers, we get:

x - 1
3
=
  
y - 2
3
=
  
z - 3
3

Final Answers

Distance = 5.1961524227066
(x - 1)/3, (y - 2)/3(z - 3)/3





What is the Answer?
Distance = 5.1961524227066
(x - 1)/3, (y - 2)/3(z - 3)/3
How does the 3-dimensional points Calculator work?
Free 3-dimensional points Calculator - Calculates distance between two 3-dimensional points
(x1, y1, z1) and (x2, y2, z2) as well as the parametric equations and symmetric equations
This calculator has 6 inputs.

What 1 formula is used for the 3-dimensional points Calculator?

Distance = Square Root ((x2 - x1)2 + (y2 - y1)2 + (z2 - z1)2)

For more math formulas, check out our Formula Dossier

What 4 concepts are covered in the 3-dimensional points Calculator?

3-dimensional points
Any three-dimensional point. Points located in R3. Example: (x, y, z)
distance
interval between two points in time
d = rt
equation
a statement declaring two mathematical expressions are equal
point
an exact location in the space, and has no length, width, or thickness
Example calculations for the 3-dimensional points Calculator
3-dimensional points Calculator Video

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