Enter Point Coordinates
Choose a 2D or 3D setup, enter two points, set your preferred rounding, and calculate the vector from point A to point B.
Example Data Table
| Case | Point A | Point B | Vector AB | Magnitude | Midpoint |
|---|---|---|---|---|---|
| 2D Example 1 | (1, 2) | (6, 8) | (5, 6) | 7.8102 | (3.5, 5.0) |
| 2D Example 2 | (-3, 4) | (2, -1) | (5, -5) | 7.0711 | (-0.5, 1.5) |
| 3D Example 1 | (2, 1, -3) | (7, 5, 1) | (5, 4, 4) | 7.5498 | (4.5, 3.0, -1.0) |
| 3D Example 2 | (0, 0, 0) | (4, -2, 9) | (4, -2, 9) | 10.0499 | (2.0, -1.0, 4.5) |
Formula Used
Vector from two points
For A(x₁, y₁, z₁) and B(x₂, y₂, z₂), vector AB = (x₂ − x₁, y₂ − y₁, z₂ − z₁). In 2D, take z-values as zero.
Magnitude and distance
|AB| = √[(x₂ − x₁)² + (y₂ − y₁)² + (z₂ − z₁)²]. This value also equals the straight-line distance between the two points.
Midpoint
Midpoint M = ((x₁ + x₂)/2, (y₁ + y₂)/2, (z₁ + z₂)/2). This marks the exact center between the starting and ending points.
Unit vector and direction
Unit vector = AB / |AB| when |AB| ≠ 0. In 3D, the unit vector entries are also the direction cosines with the coordinate axes.
How to Use This Calculator
1. Select 2D or 3D coordinates depending on your problem.
2. Enter the coordinates of point A, which is the starting point.
3. Enter the coordinates of point B, which is the ending point.
4. Choose the number of decimal places you want displayed.
5. Click Calculate Vector to show the result above the form.
6. Use the export buttons to save the detailed output as CSV or PDF.
FAQs
1. What does a vector from points represent?
It represents the directed change from the first point to the second. The vector tells you how far to move along each axis to travel from A to B.
2. Why does the order of points matter?
Reversing the points changes the sign of every component. Vector AB points from A to B, while vector BA points in the opposite direction.
3. What happens if both points are the same?
The result becomes the zero vector. Its magnitude is zero, but its unit vector and direction angles are undefined because there is no movement direction.
4. Is the magnitude the same as distance?
Yes. For a vector formed by two points, the magnitude equals the straight-line distance between those points in the selected coordinate space.
5. When should I use 2D instead of 3D?
Use 2D when your problem only involves x and y coordinates. Use 3D when depth or a z-coordinate is part of the geometry.
6. What is a unit vector?
A unit vector has magnitude one and shows direction only. It is found by dividing each vector component by the vector magnitude.
7. What are direction cosines in 3D?
Direction cosines are the cosine values of the angles between the vector and the x, y, and z axes. They describe orientation in space.
8. Can I use decimal or negative coordinates?
Yes. The calculator accepts positive, negative, and decimal coordinate values, making it suitable for classroom problems and analytical work.