\[ \frac{ {\bf v} }{ v } = \bigl( \frac{ v_x }{ v },\ \frac{ v_y }{ v },\ \frac{ v_z }{ v }\ \bigr) \\ \] \[ \vec{OT} \times \vec{OP} = ( T_x,\ T_y,\ T_z ) \times (P_x,\ P_y,\ P_z )\\ \ \\ = (T_y\ P_z - T_z\ P_y,\ \ T_z\ P_x - T_x\ P_z,\ \ T_x\ P_y - T_y\ P_x ) \\ \ \\ = (T_y\ P_z - T_z\ P_y,\ \ T_z\ P_x - 0\ P_z,\ \ 0\ P_y - T_y\ P_x ) \\ \ \\ = (T_y\ P_z - T_z\ P_y,\ \ T_z\ P_x,\ \ - T_y\ P_x ) \\ \] \[ | \vec{OT} \times \vec{OP} | = | \vec{OT} |\ | \vec{OP} |\ sin( \pi / 2 ) = R^2 \] よって， \[ \frac{ v_x }{ v } = \frac{ T_y\ P_z - T_z\ P_y }{ R^2 } \\ \frac{ v_y }{ v } = \frac{ T_z\ P_x }{ R^2 } \\ \frac{ v_z }{ v } = - \frac{ T_y\ P_x }{ R^2 } \]