The coordinates $(x,y,z)$ of two points $C$ and $D$ are $(2,7,-2)$ and $(-4,4,-8)$. Find the distance and displacement vector from $C$ to $D$.
From a solution I found online the distance equals the displacement vector $\big(-4-2,\; 4-7,\; -8-(-2)\big)$.
Displacement is shortest distance travelled unlike distance which is total distance. In which case can we say that these two values will be different?
The displacement vector from point $ C$ to $D$ will be
$\vec r=\vec r_D-\vec r_C$
$\vec r=(-4\hat i+4\hat j -8\hat k)-(2\hat i+7\hat j -2\hat k)$
$\vec r=(-6\hat i-3\hat j -6\hat k)$
The distance between these two points is the magnitude of this displacement vector and is equal to $9$ units