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AP EAMCET202022 Sep 2020Evening ShiftMathematicsThree Dimensional GeometryActual

The foot of perpendicular from (5,7,3) to the join of (9,13,15) and (12,21,10) is

Options

  1. A(-2,-19,7)
  2. B(2,19,7)
  3. C(2,2,3)
  4. D(9,13,15)

Correct answer

D. (9,13,15)

Step-by-step solution

Let A=(9,13,15) aligned & B=(12,21,10) & P=(5,7,3) and Q=(x, y, z) aligned Dr's of A B =(9-12,13-21,15-10) =(-3,-8,5)=(3,8,-5) Equation of line A B is aligned x-9 3 & = y-13 8 = z-15 -5 = x-9 3 & = , y-13 8 = , z-15 -5 = aligned aligned & x=3 +9, y=8 +13, z=-5 +15 & Q=(3 +9,8 +13,-5 +15) aligned Dr's of P Q =(3 +9-5,8 +13-7,-5 +15-3) Dr's ^ of P Q =(3 +4,8 +6,-5 +12) Since, A B P Q aligned a₁ a₂+b₁ b₂+c₁ c₂ & =0 3(3 +4)+8(8 +6)-5(-5 +12) & =0 9 +12+64 +48+25 -60 & =0 =0 aligned Put, =0 in Q Q=(9,13,15) Foot of Perp

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