The points A(1, -2, 4), B(3, 5, 7), C(4, 6, 8) are three of four vertices of parallelogram ABCD. Determine the coordinates of vertex D

Could someone please tell me to go about solving this question. Thanks a lot.

To determine the coordinates of vertex D, we need to find the fourth vertex of the parallelogram ABCD.

A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length. In this case, we have the coordinates of three vertices: A(1, -2, 4), B(3, 5, 7), and C(4, 6, 8).

To find the coordinates of D, we need to determine the vector that connects A to B and then add it to the coordinates of C. The vector connecting A to B can be found by subtracting the coordinates of A from the coordinates of B.

So, let's find the vector connecting A to B:

Vector AB = (x2 - x1, y2 - y1, z2 - z1)
= (3 - 1, 5 - (-2), 7 - 4)
= (2, 7, 3)

Now, we can add this vector to the coordinates of C to find the coordinates of D:

D = C + Vector AB
= (4, 6, 8) + (2, 7, 3)
= (4 + 2, 6 + 7, 8 + 3)
= (6, 13, 11)

Therefore, the coordinates of vertex D are (6, 13, 11).