1. Let P be point such that PA = PB - (1) 4 coordinates of P be (x, 4, z ) E ?? given - A = (7, - 8, - 9) , B = ( - 6, 4,- 12). Now, PA = 1 (x-7)2 + (8 (4+ 8)2 + (2+9)2 PB = J ( x + 6 ) 2 + (4 - 4 ) 2 + (2+ 12)2 from (1) ( 2- 7) + (4+ 8 ) + (2+ 9)2 = ( 2+6 )2 + (4-4)2+ (2+12)2 on, ( x - 7 72 + (4+ 8)2+ (2+9)2 = (2+6)2+ (y-4)2+ (2+12)2 on , x 2 + 42 + 2 2 + 49 + 64+ 81 - 14x + 164 + 182 = x 2 + y 2+2 2+ 36+ 16 + 144+ 12x-84+242. 07 194 - 142 + 164 + 182 = 196 + 122 - 8y+ 242 - 2 = 26x-244+ 62 -1 = 13x-124 +32. 13x - 124 + 32 +1=0. This is the required equation . This equation represents a plane. . Paints lying on this plane will be equidistant from A RB.(8) Find and simplify an equation for the set of all points equidistant from the points A(-1, 3, 2) and B (7, 0, -4)