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AP EAMCET202422 May 2024Morning ShiftMathematicsThree Dimensional GeometryActual

The orthocentre of triangle formed by points: (2,1,5) , (3,2,3) and (4,0,4) is

Options

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

Correct answer

C. (3,1,4)

Step-by-step solution

A(2,1,5), B(3,2,3) and C(4,0,4) Equation of line A C x-2 2 = y-1 -1 = z-5 -1 Equation line B C x-3 1 = y-2 -2 = z-3 1 Equation of altitude from A on B CP is foot of perpendicular of A P on B C aligned & P (r+3,-2 r+2, r+3) & D.R.'s of A P=(r+1,-2 r+1, r-2) & A P B C (r+1) 1+(-2 r+1)(-2)+(r+2) 1=0 & r= 1 2 P= ( 7 2 , 1, 7 2 ) aligned Equation of line A P x-2 -1 = y-1 0 = z-5 1 ....(iii) Similarly, let Q be foot of perpendicular from B to A C . Q (3, 1 2 , 9 2 ) Equation of line B Q is x-3 0 = y-2 3 = z-3 -3 ....(iv)

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