Distance between (3,4,5) and (5,6,7)

Enter point 1

(x1: , y1: z1: )

Enter point 2

(x2: y2: z2: )
  

Calculate the distance between:

(3, 4, 5) and (5, 6, 7)

Also calculate the parametric and symmetric forms

Distance formula for 3-D points

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

Distance = √(5 - 3)2 + (6 - 4)2 + (7 - 5)2

Distance = √22 + 22 + 22

Distance = √4 + 4 + 4

Distance = √12

Distance = 3.4641016151378

Parametric Equation Form:

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

Plugging in our numbers, we get:

(x,y,z) = (3,4,5) + t(5 - 3,6 - 4,7 - 5)

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

x = 3 + 2t

y = 4 + 2t

z = 5 + 2t

Symmetric Equation Form:

x - x0
a
=
  
y - y0
b
=
  
z - z0
c

Plugging in our numbers, we get:

x - 3
2
=
  
y - 4
2
=
  
z - 5
2

Final Answers

Distance = 3.4641016151378
(x - 3)/2, (y - 4)/2(z - 5)/2





What is the Answer?
Distance = 3.4641016151378
(x - 3)/2, (y - 4)/2(z - 5)/2
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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