If A (1,0,2), B (2,1,0), C (2,-5,3), D (0,3,2) are four points and the point of intersection of the lines AB and CD is P (a, b, c) , then a+b+c=

Step-by-step solution

A (1,0,2), B (2,1,0), C (2,-5,3), D (0,3,2) Eq. of line AB is x-1 1 = y 1 = z-2 -2 = ....(i) Eq. of line CD is x-2 -2 = y+5 8 = z-3 -1 = ....(ii) x= +1, y= , z=-2 +2 [From (i)] and x=-2 +2, y=8 -5, z=- +3 [From (ii)] Solving for and we get = 3 5 , = 7 5 x= 12 5 , y= 7 5 , z= -4 5 P (a, b, c)= ( 12 5 , 7 5 , -4 5 ) a+b+c=3