3.3.43 Line and Plane in Space

Condition: Ray of Light goes along the straight \ (l_ {1} \), set as the crossing line of two planes, and is reflected from the straight line \ (l_ {2} \), also set as the crossing line of the two planes. Find the guide vector of a straight line along which the reflected beam will go. \ [\ Begin {Array} {l} L_ {1}: \ Left \ {\ Begin {Array} {C} X+Y-Z-2 = 0 \\ 3 X+2 Y+3 Z-13 = 0 \ END} \ RIIRHT. \\ l_ {2}: \ left \ {\ begin {array} {l} x+18 y-2 z-85 = 0 \\ 2 x+15 y-z-71 = 0 \ End {Array} \ Right. \ end {Array} \]