question_answer 33)

Show that the line joining the origin to the plane (2, 1, 1) is perpendicular to the line determined by the points (3, 5, –1), (4, 3, –1). 

Answer:

Equation of line joining points (0, 0, 0) and (2, 1, 1) is given by             i.e.,       Also equation of line joining points (3, 5, ?1) and       (4, 2, ?1) is given by             i.e.       Now direction ratios of line L1 are 2, 1, 1 and direction ratios of line L2 are 1, ?2, 0       As 2 × 1 + 1 × (?2) + 1 × 0 = 2 ? 2 = 0        Lines L1 and L2 are perpendicular to each other.