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AP EAMCET202420 May 2024Morning ShiftMathematicsThree Dimensional GeometryActual

Let 0( 0 ), A ( i +2 j + k ), B (-2 i +3 k ), C (-2 i + j ), D (4 k ) are position vectors of the points O , A , B , C and D , If a line passing through A and B intersects the plane passing through O , C and D at the point R . then position vector of R is

Options

  1. A-8 i -4 j +7 k
  2. B2 i + j + k
  3. C-7 i -6 j -5 k
  4. D3 i +2 j -5 k

Correct answer

A. -8 i -4 j +7 k

Step-by-step solution

Equation of line passing through A( i +2 j +k) and B(-2 i +3 k ) is = i +2 j + k + (-3 i -2 j +2 k ) =(1-3 ) i +(2-2 ) j +(1+2 ) k ....(i) Equation of plane passing through O( 0 ), C(2 i + j ), D(4 k ) Normal vector perpendicular to plane OCD is n = O C O D = | array ccc i & j & k 2 & 1 & 0 0 & 0 & 4 array |=4 i -8 j Equation of plane OCD is ( r - 0 ) n =0 r n =0 4 x-8 y=0 ....(ii) From (i) x=1-3 , y=2-2 , z=1+2 Put in (ii) 4(1-3 )-8(2-2 )=0 =3 x=-8, y=-4, z=7 R=-8 i -4 j +7 k

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