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Question

The three vertices of a parallelogram PQRS are P(3,-1,2), Q(1,2,-4), R(-1,1,2). Then, the coordinates of the fourth vertex is .

A
(-1,-2,8)
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B
(1, 2,8)
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C
(1,-2,8)
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D
(1,-2,-8)
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Solution

The correct option is C (1,-2,8)
Let the coordinates of the fourth vertex S be (x,y,z).
Since, the diagonals of a parallelogram bisect each other.
So,the mid-points of PR and QS will coincide.
(312,1+12,2+22)=(1+x2,2+y2,4+z2)(1,0,2)=(x+12,y+22,z42)x+12=1,y+22=0 and z42=2x=1,y=2 and z=8

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