To calculate the distance between two points:
\[ D = \sqrt{ (X2 - X1)^2 + (Y2 - Y1)^2 + (Z2 - Z1)^2 } \]
Where:
The distance between two points in a three-dimensional space is the straight-line distance calculated using the formula above. It measures the length of the shortest path connecting the two points.
Example 1:
Assume the coordinates of Point 1 are (2, 3, 4) and the coordinates of Point 2 are (5, 7, 1). Using the formula:
\[ D = \sqrt{ (5 - 2)^2 + (7 - 3)^2 + (1 - 4)^2 } = \sqrt{ 3^2 + 4^2 + (-3)^2 } = \sqrt{ 9 + 16 + 9 } = \sqrt{ 34 } \approx 5.83 \]
The distance between the points is approximately 5.83 units.
Example 2:
Assume the coordinates of Point 1 are (-1, -1, -1) and the coordinates of Point 2 are (2, 2, 2). Using the formula:
\[ D = \sqrt{ (2 - (-1))^2 + (2 - (-1))^2 + (2 - (-1))^2 } = \sqrt{ 3^2 + 3^2 + 3^2 } = \sqrt{ 27 } \approx 5.20 \]
The distance between the points is approximately 5.20 units.
