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Most Important Selected Qs for JEE AdvancedMathematicsThree Dimensional Geometry

Paragraph The base of a pyramid is rectangular, three of its vertices of the base are A (2,2,-1), B (3,1,2) and C (1,1,1) (may or may not be in order). Its vertex at the top is P (4,- 26 3 ,- 10 3 ) and fourth vertex of the base is D. On the basis of above information, answer the following : Question Co-ordinates of foot of the normal drawn from P on the base of the pyramid are -

Options

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

Correct answer

A. (2, 4 3 , 2 3 )

Step-by-step solution

Equation of the base a(x-1)+b(y-1)+c(z-1)=0 which also passes through A (2,2,-1) and B (3,1,2) a+b-2 c=0 ...(i)2 a+c=0...(ii) aligned & c=-2 a, b=-5 a & a(x-1)-5 a(y-1)-2 a(z-1)=0 aligned x-5 y-2 z+6=0 foot of the normal from P x-4 1 = y+ 26 3 -5 = z+ 10 3 -2 x-4 1 = y+ 26 3 -5 = z+ 10 3 -2 =-2 x=2, y= 4 3 , z= 2 3 (2, 4 3 , 2 3 )

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