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MHT CET20242 May 2024Evening ShiftMathematicsThree Dimensional GeometryActual

The equation of the line, through A(1,2,3) and perpendicular to the vector 2 i + j - k and i +3 j +2 k , is

Options

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

Correct answer

D. r =( i +2 j +3 k )+ ( i - j + k )

Step-by-step solution

Let a = i +2 j +3 k , aligned & b =2 i + j - k & c = i +3 j +2 k aligned b c is perpendicular to both b and c . b c = | array ccc i & j & k 2 & 1 & -1 1 & 3 & 2 array |=5 i -5 j +5 k The direction ratios of the required line are 5,-5,5 i.e. 1,-1,1 The required equation of line is r = i +2 j +3 k + ( i - j + k )

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