A line having direction ratios 1,-4,2 intersects the lines x-7 3 = y-1 -1 = z+2 1 and x 2 = y-7 3 = z 1 at the points A and B resp., then co-ordinates of points A and B are

Step-by-step solution

Let x-7 3 = y-1 -1 = z+2 1 = x=3 +7, y=- +1, z= -2 Let x 2 = y-7 3 = z 1 = x=2 , y=3 +7, z= Co-ordinates of a point on the first line are A (3 +7,1- , -2) Co-ordinates of a point on the second line are B (2 , 3 +7, ) D.r.s. of A B are 3 -2 +7,- -3 -6, - -2 D.r.s. of A B are 1,-4,2 aligned & 3 -2 +7 1 = - -3 -6 -4 = - -2 2 & 3 -2 +7= +3 +6 4 & - +2=0 ...(i) & +3 +6 4 = - -2 2 & -5 -10=0...(ii) aligned Solving (i) and (ii), we get aligned & =-5, =-3 & A (-8,6,-7), & B (-6,-2,-3) aligned