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MHT CET202121 Sep 2021Evening ShiftMathematicsThree Dimensional GeometryActual

The equations of a line passing through (3,-1,2) and perpendicular to the lines r =( i + j - k )+ (2 i -2 j + k ) and r =(2 i + j -3 k )+ ( i -2 j +2 k ) is

Options

  1. Ax-3 2 = y+1 3 = z-2 2
  2. Bx-3 3 = y+1 2 = z-2 2
  3. Cx+3 2 = y+1 3 = z-2 2
  4. Dx-3 2 = y+1 3 = z-2 3

Correct answer

A. x-3 2 = y+1 3 = z-2 2

Step-by-step solution

Let a, b, c be the direction ratios of the required line. 2 a -2 ~b + c =0 ... (1) and a-2 b+2 c=0 From (1) and (2), we write aligned & a | array ll -2 & 1 -2 & 1 array | = b | array ll 2 & 1 1 & 2 array | = c | array ll 2 & -2 1 & -2 array | a -2 = b -3 = c -2 & ( a , b , c )=(2,3,2) aligned So equation of required line is x-3 2 = y+1 3 = z-2 2

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