Calculate the distance between:
(-1, 2, -3) and (4, 6, 8)
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 + (6 - 2)2 + (8 - -3)2
Distance = √52 + 42 + 112
Distance = √25 + 16 + 121
Distance = √162
Distance = 12.727922061358
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 - -1,6 - 2,8 - -3)
(x,y,z) = (-1,2,-3) + t(5,4 ,11)
x = -1 + 5t
y = 2 + 4t
z = -3 + 11t
Symmetric Equation Form:
| x - x0 | |
| a |
| = |
| y - y0 | |
| b |
| = |
| z - z0 |
| c |
Plugging in our numbers, we get:
| x - -1 | |
| 5 |
| = |
| y - 2 | |
| 4 |
| = |
| z - -3 |
| 11 |
Final Answers
Distance = 12.727922061358
(x - -1)/5, (y - 2)/4(z - -3)/11
(x - -1)/5, (y - 2)/4(z - -3)/11
What is the Answer?
Distance = 12.727922061358
(x - -1)/5, (y - 2)/4(z - -3)/11
(x - -1)/5, (y - 2)/4(z - -3)/11
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
