The coordinates of the 'other vector' are
x(theta, phi) = X0 + D * sin(theta) * cos(phi)
y(theta, phi) = Y0 + D * sin(theta) * sin(phi)
z(theta, phi) = Z0 + D * cos(theta)
where
D
is the dinstance,
theta
and
phi
have arbitrary values.
That means you have not a single vector at distance
D
but infinite (squared!) ones. If you like you may assign values to
theta
and
phi
to pick one of them.