Symmetry of a 3D point A by a line made of 2 points B and C

Question

Given a point A of coordinates $(a_1,b_1,c_1)$ and two points $B(x_1,y_1,z_1)$ and $C (x_2,y_2,z_2)$

What are the coordinates of $D(a_2,b_2,c_2)$ symmetry of A by the line BC?

Answer 1

If $D$ is symmetry of $A$ by line $BC$, then $ABDC$ is a parallelogram.

$\vec{A}+\vec{D}=\vec{B}+\vec{C}$

From there You can manage.