Solution
= Solution
\b[False.] With $(x,t)$ coordinates, take
$$
A=(0,0),\qquad B=(1,1),\qquad C=(-1,1).
$$
Both separations from $A$ are lightlike, but $B-C=(2,0)$ is spacelike.
= Solution
\b[False.] With $(x,t)$ coordinates, take
$$
A=(0,0),\qquad B=(1,1),\qquad C=(-1,1).
$$
Both separations from $A$ are lightlike, but $B-C=(2,0)$ is spacelike.