Calculatrice de Magnitude de Vecteur Gratuite
Calculez la magnitude (norme) d'un vecteur 2D ou 3D. Trouvez la longueur du vecteur avec la formule euclidienne.
Magnitude
5.000000
Formule
Vector Magnitude
Formula
For 2D vectors (z = 0): A unit vector has magnitude 1 and points in the same direction: v_hat = v /v = sqrt(x² + y² + z²) v = sqrt(x² + y²) Unit Vector
v = (x/ v , y/ v , z/ v
Direction (2D)
The angle from the positive x-axis: theta = arctan(y/x)
Exemple Résolu
Find the magnitude and unit vector of (3, 4, 0).
- 01|v| = √(9 + 16 + 0) = √25 = 5
- 02Unit vector = (3/5, 4/5, 0) = (0.6, 0.8, 0)
- 03Direction = arctan(4/3) ≈ 53.13°
Questions Fréquentes
What is vector magnitude?
The magnitude (or length) of a vector is the distance from the origin to the point it represents. It is always non-negative.
What is a unit vector?
A unit vector has a magnitude of exactly 1. It indicates direction only. Any nonzero vector can be normalized to a unit vector by dividing by its magnitude.
How do I find the distance between two points?
Form a vector from one point to the other by subtracting coordinates, then find the magnitude. distance = √((x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²).
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