\[ \begin{aligned} y_a + v_{ay} \frac{x_b - x_a}{v_{ax} - v_{bx}} &= y_b + v_{by} \frac{x_b - x_a}{v_{ax} - v_{bx}} \\ z_a + v_{az} \frac{x_b - x_a}{v_{ax} - v_{bx}} &= z_b + v_{bz} \frac{x_b - x_a}{v_{ax} - v_{bx}} \\ v_{bx}^2 + v_{by}^2 + v_{bz}^2 &= s_b^2 \end{aligned} \]