Vector Calculator with Terminal Point

Vector Calculator Form

Mode

Vector Name

Unit Label

Initial X₁

Initial Y₁

Initial Z₁

Terminal X₂

Terminal Y₂

Terminal Z₂

Decimal Precision

Example Data Table

Mode	Initial Point	Terminal Point	Vector Components	Magnitude	Unit Vector
3D	(1, 2, 3)	(5, 7, 9)	<4, 5, 6>	8.775	<0.456, 0.570, 0.684>
2D	(-2, 1)	(4, 5)	<6, 4>	7.211	<0.832, 0.555>
3D	(0, 0, 0)	(3, -4, 12)	<3, -4, 12>	13	<0.231, -0.308, 0.923>

Formula Used

Vector from initial point to terminal point
R = <x₂ - x₁, y₂ - y₁, z₂ - z₁>

Magnitude of the vector
|R| = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]

Unit vector
û = R / |R|

Midpoint between points
M = ((x₁ + x₂)/2, (y₁ + y₂)/2, (z₁ + z₂)/2)

Direction angles in 3D
cos α = Rx / |R|, cos β = Ry / |R|, cos γ = Rz / |R|

2D slope and azimuth
slope = Δy / Δx and θ = atan2(Δy, Δx)

How to Use This Calculator

Select 2D or 3D mode.
Enter the initial point coordinates.
Enter the terminal point coordinates.
Set the decimal precision you want.
Optionally add a vector name and unit label.
Click Calculate Vector.
Read the result summary above the form.
Review the graph, export CSV, or generate a PDF report.

Frequently Asked Questions

1) What does terminal point mean in vector problems?

The terminal point is the ending point of the vector. The vector begins at the initial point and ends at the terminal point. Subtracting the initial coordinates from the terminal coordinates gives the vector components.

2) How are vector components calculated from two points?

Subtract each initial coordinate from its matching terminal coordinate. In 2D, use Δx and Δy. In 3D, use Δx, Δy, and Δz. These differences form the component vector.

3) What is the magnitude of a vector?

The magnitude is the vector length. It measures the straight-line distance between the initial and terminal points. In physics, it often represents displacement size, distance scale, or resultant strength.

4) Why is the unit vector useful?

A unit vector shows direction only. Its magnitude equals one. It is useful when you want the pure direction of motion, force, velocity, or displacement without keeping the original length.

5) What happens if both points are identical?

If the initial and terminal points are the same, the vector becomes a zero vector. Its magnitude is zero, and the unit vector and direction angles are undefined because no direction exists.

6) What is azimuth in this calculator?

Azimuth is the horizontal direction angle measured from the positive x-axis using the vector projection in the x-y plane. It helps describe direction in navigation, mechanics, and coordinate analysis.

7) Can I use this calculator for displacement in physics?

Yes. A displacement vector is found exactly this way. Enter the starting position as the initial point and the ending position as the terminal point. The result gives direction and displacement magnitude.

8) What is shown in the graph?

The graph plots the initial point, terminal point, and the line joining them. This makes the vector direction easy to inspect visually and helps confirm the coordinate differences used in the calculation.