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AP EAMCET201726 Apr 2017Morning ShiftMathematicsThree Dimensional GeometryActual

A B C is formed by A(1,8,4), B(0,-11,4) and C(2,-3,1) . If D is the foot of the perpendicular from A to B C . Then the coordinates of D are

Options

  1. A(– 4, 5, 2)
  2. B(4, 5, – 2)
  3. C(4, – 5, 2)
  4. D(4, – 5, – 2)

Correct answer

B. (4, 5, – 2)

Step-by-step solution

The vertices of A B C are given as A(1,8,4) , B(0,-11,4) and C(2,-3,1) . Equation of line B C , x 2 = y+11 8 = z-4 -3 = (say) As point D is on line B C , so coordinates of D are (2 , 8 -11,-3 +4) Since, A D B C aligned & A D B C=0 & (2 -1,8 -19,-3 ) (2,8,-3)=0 & 2(2 -1)+8(8 -19)+(-3)(-3 )=0 & 4 -2+64 -152+9 =0 & 77 =154 & =2 aligned Hence, the coordinates of D are (4,5,-2)

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