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AP EAMCET201923 Apr 2019Morning ShiftMathematicsThree Dimensional GeometryActual

The distance between the orthocentre and circumcentre of the triangle formed by the points ((1,2,3),(3,-1,5) ) and ((4,0,-3) ) is

Options

  1. A( 33 2 )
  2. B( 31 2 )
  3. C( 27 2 )
  4. D( 23 2 )

Correct answer

A. ( 33 2 )

Step-by-step solution

Let (A=(1,2,3) ) ( aligned B & =(3,-1,5) C & =(4,0,-3) D R^ S of A B & =(2,-3,2) D R^ ' of B C & =(1,1,-8) D R^ S of A C & =(3,-2,-6) aligned ) Here, we noticed that ( A B A C ) ( A=90^ ) Orthocentre of ( A B C= ) vertex (A ) (H=(1,2,3) ) Circumcentre of ( A B C= ) mid-point of ( B C ) (S= ( 7 2 , -1 2 , 1 ) ) ( ) Required distance ((H S)= 33 2 ) ( aligned & ( 7 2 -1 )^2+ (- 1 2 -2 )^2+(1-3)^2 & = 25 4 + 25 4 +4 = 66 4 aligned ) Hence, answer is (a).

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