Answer :

the vertices of the parallelogram be A(3, 4, -3), B(7, 10, -3) and C(5, -2, 7), and the fourth coordinate be D(a,b,c).

the property of parallelogram is the diagonal bisect each other. Therefore,

diagonal AC and BD will bisect each other, and the bisecting point will be equal to the two diagnals. By using section formula, we get

, where m and n are 1 and 1.

Finding the coordinate of mid point of diagonal AC,

= (4,1,2)

Now, Finding the coordinate of mid point of diagonal BD,

Equating the two mid points, we get

. Thus,


8 = a + 7

a = 1

b + 10 = 2

b = -8


c = 7

therefore the point is ( 1, -8, 7).

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