Given :
The vertices of parallelogram ABCD are A(4,0,3), B(3,4,-2),C(-2,0,1).
To Find :
The coordinates of fourth vertices.
Solution :
We know, the vertices are ABCD .
Let, point D is (x,y,z) .
Also, diagonals of a parallelogram bisect each other.
Let, point of intersection of daigonal is O.
Coordinates of O are :
[tex]O_x = \dfrac{4+(-2)}{2}= 1\\\\O_y = \dfrac{0+0}{2 } = 0 \\\\O_z = \dfrac{3+1}{2}= 2[/tex]
O(1,0,2)
Value of point O through BD.
[tex]O_x = \dfrac{3+x}{2}\\\\x=-1\\\\O_y = \dfrac{4+y}{2}\\\\y = -4\\\\O_z= \dfrac{-2+z}{2}\\\\z = 6[/tex]
Therefore, the fourth vertices is D( -1,-4,6 ).
