1. **Stating the problem:** We want to calculate the vector between two points, each given by latitude ($\phi$), longitude ($\lambda$), and altitude ($h$). 2. **Convert geodetic coordinates to Earth-Centered, Earth-Fixed (ECEF) Cartesian coordinates:** Given the point $(\phi, \lambda, h)$, convert to ECEF $(x,y,z)$ using $$ N = \frac{a}{\sqrt{1 - e^2 \sin^2 \phi}} $$ where $a$ is the Earth's equatorial radius and $e$ is the Earth's eccentricity. Then: $$ x = (N + h) \cos \phi \cos \lambda $$ $$ y = (N + h) \cos \phi \sin \lambda $$ $$ z = \left( N(1 - e^2) + h \right) \sin \phi $$ 3. **Calculate the vector difference:** If points $P_1$ and $P_2$ have coordinates $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$ in ECEF, the vector from $P_1$ to $P_2$ is $$ \vec{v} = (x_2 - x_1, y_2 - y_1, z_2 - z_1) $$ 4. **Explanation:** This vector represents the straight line in 3D Cartesian space between the two real-world points, accounting for Earth’s curvature and altitude. 5. **Summary:** - Convert $(\phi, \lambda, h)$ of both points to ECEF - Subtract their ECEF coordinates - The result is the vector between them in meters (or units consistent with $a$ and $h$) This process transforms geographic coordinates into a Cartesian vector suitable for spatial calculations.