como tirar calcular a distância entre duas retas

Exemplo:

\[\eqalign{ & r:X = \left( {1,1,1} \right) + t\left( {1,2,3} \right) \cr & s:X = \left( {1,2,4} \right) + h\left( {2,4,6} \right) \cr & P = \left( {1,2,4} \right) \cr & Q = \left( {1 + t,1 - 2t,1 + 3t} \right) \cr & \overrightarrow {PQ} = Q - P = \left( {t,2t - 1,3t - 3} \right) \cr & \overrightarrow {PQ} \cdot \overrightarrow r = 0 = t = {{11} \over {14}} \cr & Q = \left( {1 + t,1 + 2t,1 + 3t} \right) = \left( {{{25} \over {14}},{{18} \over 7},{{47} \over {14}}} \right) \cr & d\left( {P,Q} \right) = \sqrt {{{\left( {1 - {{25} \over {14}}} \right)}^2} + {{\left( {2 - {{18} \over 7}} \right)}^2} + {{\left( {4 - {{47} \over {14}}} \right)}^2}} = {{\sqrt {266} } \over {14}} }\]