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AP EAMCET202021 Sep 2020Morning ShiftMathematicsStraight LinesActual

The feet of perpendicular from the point (A(1,0,3) ) to the join of the points (B(4,7,1) ) and (C(3,5,3) ) is

Options

  1. A( ( 5 3 , 7 3 , 17 3 ) )
  2. B( ( 10 3 , 17 3 , 6 3 ) )
  3. C( (0, 1 2 , 3 2 ) )
  4. D( ( 1 5 , 3 5 , 7 5 ) )

Correct answer

A. ( ( 5 3 , 7 3 , 17 3 ) )

Step-by-step solution

Since equation of line joining points (B(4,7,1) ) and (C(3,5,3) ) is ( aligned x-4 4-3 & = y-7 7-5 = z-1 1-3 x-4 1 & = y-7 2 = 3-1 -2 = (let) ...(i) aligned ) Now the general point over the above line (i) is (P( +4,2 +7,1-2 ) ) Let point (P ) is the foot of perpendicular of point (A(1,0,3) ) over the line (i), so AP ( ) line ( aligned & ( +4-1)(1)+(2 +7-0)(2)+(1-2 -3)(-2)=0 & +3+4 +14+4 +4=0 9 +21=0 & =- 7 3 aligned ) ( ) The coordinate of point (P ) is ( (4- 7 3 , 7- 14 3 , 1+ 14 3 )= ( 5 3 , 7 3 , 17 3 ) ) Hence,

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