question_answer 54)

Show that the lines x = ay + b, z = cy + d and x = a’y + b’, z = c’y + d’ are perpendicular to each other, if aa’ + cc’ + 1 + 0. 

Answer:

Given equations of lines is x = ay + b, z + cy + d              equation of given in symmetrical form is                               ?.(1)       Again given equation of lien is x = a?y + b?, z = c?y + d?        equation of given line in symmetrical form is                            ?(2)       Also direction ratios of line (1) and (2) are respectively a, 1, c are a?, 1, c?       Since it is given that lines are perpendicular, so              a × a? + 1 × 1+ c × c? = 0       i.e., aa? + cc? + 1 = 0       which is proved.