The vector magnitude formula uses the square root of the sum of squared components because it is a direct application of the Pythagorean theorem. When a vector is drawn in a Cartesian plane, its horizontal and vertical components form the legs of a right triangle, and the vector itself is the hypotenuse.
Conditions: The vector is represented in an orthonormal Cartesian coordinate system.; The components correspond to perpendicular displacements.; The magnitude is the Euclidean length of the vector.
The vector magnitude formula uses the square root of the sum of squared components because it is a direct application of the Pythagorean theorem. When a vector is drawn in a Cartesian plane, its horizontal and vertical components form the legs of a right triangle, and the vector itself is the hypotenuse.
Conditions: The vector is represented in an orthonormal Cartesian coordinate system.; The components correspond to perpendicular displacements.; The magnitude is the Euclidean length of the vector.