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
(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
(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.
(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)
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
