Vector Magnitude

Vector Magnitude in 3D

The magnitude (or length) of a vector $\mathbf{v} = (x, y, z)$ is:

$|\mathbf{v}| = \sqrt{x^2 + y^2 + z^2}$

This is a direct extension of the Pythagorean theorem into three dimensions.

Unit Vectors

A vector with magnitude 1 is called a unit vector. To normalize any vector:

$\hat{\mathbf{v}} = \frac{\mathbf{v}}{|\mathbf{v}|} = \left(\frac{x}{|\mathbf{v}|},\; \frac{y}{|\mathbf{v}|},\; \frac{z}{|\mathbf{v}|}\right)$

Unit vectors indicate direction only.

Distance Between Points

The distance between $P_1 = (x_1, y_1, z_1)$ and $P_2 = (x_2, y_2, z_2)$ is the magnitude of their difference:

$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2}$

Examples

Your Task

Implement double vec_length3(double x, double y, double z) that returns the 3D vector magnitude.

Use #include <math.h> and the sqrt function.