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AP EAMCET202119 Aug 2021Evening ShiftMathematicsVector AlgebraActual

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

Options

  1. A( 3 , 3 , 1 )
  2. B( 3 , 1 , 3 )
  3. C( 1 , 3 , 3 )
  4. D( 0 , 0 , 0 )

Correct answer

A. ( 3 , 3 , 1 )

Step-by-step solution

We have a parallelogram A B C D , whose vertices are A 2 , 4 , - 1 ,   B 3 , 6 , - 1 ,   C 4 , 5 , 1 Now, assume the fourth vertex D x , y , z So, we have diagonals A C and B D Now, we know that, diagonals of a parallelogram bisect each other, So, coordinate of E , as mid-point of A C is 3 ,   9 2 ,   0     . . . 1 As mid-point of B D is x + 3 2 ,   y + 6 2 ,   z - 1 2       . . . 2 So, comparing 1 and 2 , x + 3 2 = 3   ⇒   x = 3 y + 6 2 = 9 2 &

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