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AP EAMCET202315 May 2023Evening ShiftMathematicsThree Dimensional GeometryActual

If A (3,-1,11), B (0,2,3), C (4,8,11) are three points, then the coordinates of the foot of the perpendicular drawn from the point A to the line joining the points B and C is

Options

  1. A(3,5,7)
  2. B(5,9,6)
  3. C(2,5,7)
  4. D(1,2,3)

Correct answer

C. (2,5,7)

Step-by-step solution

Given A (3,-1,11), B (0,2,3) and C (4,8,11) Now, Equation of BC is aligned & x-0 4 = y-2 6 = 2-3 8 = & x=4 r, y=6 r+2, z=8 r+3 aligned Any point on BC (4 r , 6 r +2,8 r +3) DR's of BC =(4-0,8-2,11-3)=(4,6,8) DR's of A P=(4 r-3,6 r+3,8 r-8) Since B C A P aligned & (4 r-3) 4+(6 r+3) 6+(8 r-8) 8=0 r= 1 2 & P(4 r, 6 r+2,8 r+3)=P(2,5,7) aligned

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