Question

Two positions on the Earth’s surface are given in the form of Cartesian coordinates in the WGS84 reference frame and ellipsoid. The norm of difference of these two position vectors is the ____________

• A. spherical distance
• B. ellipsoidal distance
• C. Euclidean distance
• D. planar distance

Hint:

When using Cartesian coordinates in the WGS84 reference frame, the straight-line distance between two points is calculated using the Euclidean norm.

Answer 1

The Correct Option is C

In the WGS84 reference frame, if positions are given as 3D Cartesian coordinates (X, Y, Z), then the norm of the difference between two such vectors is computed using:

\[ \| \vec{r_1} - \vec{r_2} \| = \sqrt{(X_1 - X_2)^2 + (Y_1 - Y_2)^2 + (Z_1 - Z_2)^2} \] This is the Euclidean distance between the two points in 3D space. It does not represent the actual curved path over the Earth's surface (spherical or ellipsoidal distance), but rather the straight-line 3D distance through space.