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AP EAMCET201822 Apr 2018Evening ShiftMathematicsThree Dimensional GeometryActual

P and Q are points on the straight line passing through the point A(3 i + j - k ) and parallel to the vector 2 i - j +2 k , If A P=A Q=3 , then the vector equation of the plane O P Q is

Options

  1. Ar =(s+5 t) i +2 s j +(t-3 s) k
  2. Br =(3 i + j - k )+s(2 i - j +2 k )+t(5 i + k )
  3. Cr =(s+5 t) i +2 s j +(5 s+t) k
  4. Dr =(3 t-s) i +2 s j +(t-3 s) k

Correct answer

A. r =(s+5 t) i +2 s j +(t-3 s) k

Step-by-step solution

Equation of line passing through the point A(3 i + j - k ) and parallel to the vector 2 i - j +2 k is, x-3 2 3 = y-1 - 1 3 = z+1 2 3 = 3 [ A P=A Q=3] So, coordinates of P and Q are (5,0,1) and (1,2,-3) . So, OP and OQ are (5 i + k ) and ( i +2 j -3 k ) Now, equation of plane O P Q , r =s( O Q )+t( O P ) r is coplanar with vectors O P and O Q =(s+5 t) i +2 s j +( t -3 s) k

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