If A(2,4,-1), B(3,6,-1) and C(4,5,1) are three consecutive vertices of a parallelogram, then its fourth vertex is

Step-by-step solution

A=(2,4,-1), B=(3,6,-1), C=(4,5,1) Let D=(x, y, z) Since, diagonals of a parallelogram are bisect each other. Mid-point of A C= Mid-point of B D aligned & ( 2+4 2 , 4+5 2 , -1+1 2 )= ( 3+x 2 , 6+y 2 , -1+z 2 ) & (3, 9 2 , 0 )= ( 3+x 2 , 6+y 2 , -1+z 2 ) & 3+x 2 =3 ; 6+y 2 = 9 2 ; -1+z 2 =0 & 3+x=6 ; 6+y=9 ;-1+z=0 & x=3 ; y=3 ; z=1 aligned Fourth vertex D=(3,3,1) . Hence, option (d) is correct.