question_answer 34)

If l1, m1, n1 and l2, m2, n2 are the direction cosines of two mutually perpendicular lines. Show that the direction cosines of the line perpendicular to both of these are m1n2 – m2n1; n1l2 – n2l1 – n1l1 ; l1 m1 – l2m1. 

Answer:

Unit vectors parallel to given lines are respectively             and       As  is a unit vector perpendicular to both unit vectors  so we compute as follows                          required direction cosines are m1n1 ? m2n1 ; n1l2 ? n2l1; l1 m2 ? l2 m1.