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Manipal MET2015MathematicsThree Dimensional Geometry

Equation of the plane that contains the lines r =( i + j )+ ( i +2 j - k ) and r =( i + j )+ (- i + j -2 k ) , is

Options

  1. Ar (2 i + j -3 k )=-4
  2. Br (- i + j + k )=0
  3. Cr (- i + j + k )=0
  4. DNone of these

Correct answer

C. r (- i + j + k )=0

Step-by-step solution

The lines are parallel to the vectors b ₁= i +2 j - k and b ₂=- i + j -2 k . The plane normal to the vector n is b ₁ b ₂= | array rrr i & j & k 1 & 2 & -1 -1 & 1 & -2 array |=-3 i +3 j +3 k The required plane passes through ( i + j ) and is normal to the vector n . Its equation is r n = a n array lc & r (-3 i +3 j +3 k )=( i + j ) (-3 i +3 j +3 k ) & r (-3 i +3 j +3 k )=-3+3 & r (- i + j + k )=0 array

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