{Bx,By,0} → {Sblx,Sbly,Sblz}, {-Bx,By,0} → {Sbrx,Sbry,Sbrz}

Solve[{(x - Rx)/(Bx - Rx) == (y - Ry)/(By - Ry) == (z - Rz)/-Rz, Tx x + Ty y + Tz z == Tx Cx + Ty Cy + Tz Cz}, {x, y, z}]