If a d - b c ≠ 0 , then the area (in sq. units) of the parallelogram formed by the lines a x + b y + 2 = 0 , a x + b y + 5 = 0 , c x + d y + 3 = 0 and c x + d y + 7 = 0 is

Step-by-step solution

Given: a x + b y + 2 = 0       . . . i a x + b y + 5 = 0       . . . . ii →   Parallel lines c x + d y + 3 = 0       . . . . iii c x + d y + 7 = 0       . . . . iv →   Parallel lines Opposite sides are parallel in parallelogram. Let d 1 be the distance between i   &   ii , then d 1 = 5 - 2 a 2 + b 2 = 3 a 2 + b 2   Let d 2 be the distance between iii   &   iv , then d 2 = 7 - 3 c 2 + d 2 = 4