Vectors in 3D
A vector has both magnitude and direction. Change its three components to explore how a vector extends through space and how its magnitude is calculated.
3D coordinate system
Drag to rotate. The arrow represents the vector from the origin.
Touch and drag to rotate the view.
X axis / component
Y axis / component
Z axis / component
Resultant vector
Magnitude |v|
5.39
Unit vector
0.557i + 0.371j + 0.743k
Component form
(3, 2, 4)
Live calculation
|v| = √(3² + 2² + 4²)
|v| = √29 ≈ 5.39
|v| = √29 ≈ 5.39
Understanding the vector
This vector moves 3 units along X, 2 units along Y and 4 units along Z. Its magnitude is the straight-line distance from the origin to the vector's endpoint.
The three components are perpendicular to one another. By the three-dimensional Pythagorean theorem, their squares add to the square of the vector's magnitude.