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
(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
(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.
(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
