How is the magnitude of a vector calculated?

The magnitude of a vector is determined by using the formula that accounts for all components of the vector in each dimensional space. In a three-dimensional Cartesian coordinate system, a vector V is often expressed in terms of its components along the x, y, and z axes, denoted as Vx, Vy, and Vz.

To find the magnitude |V| of the vector, the appropriate formula is given by the square root of the sum of the squares of its components. This accounts for the contributions of each direction to the overall length of the vector. Specifically, the calculation involves squaring each component (Vx, Vy, and Vz), summing these squared values, and then taking the square root of the resulting sum:

|V| = sqrt(Vx^2 + Vy^2 + Vz^2).

This formulation is derived from the Pythagorean theorem and ensures that the distance represented by the vector is accurately portrayed in space. If we were only considering two-dimensional vectors, the formula would reduce to the case with Vz set to zero, but in three dimensions, all three components must be included to obtain the true magnitude. Thus, the correct choice reflects this comprehensive approach to calculating a vector's magnitude in three-dimensional