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Question: Answered & Verified by Expert
If the points (2,4,-1),(3,6,-1) and (4,5,1) are three consecutive vertices of a parallelogram, then its fourth vertex is
MathematicsVector AlgebraAP EAMCETAP EAMCET 2021 (19 Aug Shift 2)
Options:
  • A (3,3,1)
  • B (3,1,3)
  • C (1,3,3)
  • D (0,0,0)
Solution:
2389 Upvotes Verified Answer
The correct answer is: (3,3,1)

We have a parallelogram ABCD,

whose vertices are A2,4,-1, B3,6,-1, C4,5,1

Now, assume the fourth vertex Dx,y,z

So, we have diagonals AC and BD

Now, we know that, diagonals of a parallelogram bisect each other,

So, coordinate of E, as mid-point of AC is 3, 92, 0  ...1

As mid-point of BD is x+32, y+62, z-12   ...2
So, comparing 1 and 2

x+32=3  x=3

y+62=92y=3 and 

z-12=0  z=1

So, the coordinate of D is 3, 3, 1.

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