सदिश परिमाण कैलकुलेटरसूत्र

Vector Magnitude

Formula

v= sqrt(x² + y² + z²)

For 2D vectors (z = 0): v= sqrt(x² + y²)

Unit Vector

A unit vector has magnitude 1 and points in the same direction:

v_hat = v /v= (x/v, y/v, z/v)

Direction (2D)

The angle from the positive x-axis: theta = arctan(y/x)

हल किया गया उदाहरण

Find the magnitude and unit vector of (3, 4, 0).

  1. |v| = √(9 + 16 + 0) = √25 = 5
  2. Unit vector = (3/5, 4/5, 0) = (0.6, 0.8, 0)
  3. Direction = arctan(4/3) ≈ 53.13°