How to calculate the unknown vector when the distance between vectors are known?

Question

$‖C-P‖=d$ Consider the above equation where $C$ and $P$ are two vectors.$C=(X,Y,Z)$ and $P=(U,V,W)$. $d$ is the distance between two vectors ($C$ and $P$). I know the vector $P=(U,V,W)$ and the distance between two vectors '$d$'. Now how to calculate the unknown vector $C=(X,Y,Z)$?

Answer 1

Note that there is no such thing as "distance between 2 vectors", any 2 vectors can be drawn from 1 initial point (say the origin) because as long as you maintain the magnitude, direction, and sense of a vector then you can move it where ever you want.

So $\|C-P\|$ actually the length of the vector $\vec a$ that is defined by $\vec a= \vec C-\vec P$

Now if you have $P(U,V,W)$ and you want to get the vector $C$ (that is not unique) you can simply consider it as $C(U+d,V,W)$.