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MHT CET202311 May 2023Morning ShiftMathematicsThree Dimensional GeometryActual

The vector equation of the line 2 x+4=3 y+1=6 z-3 is

Options

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

Correct answer

B. r = (-2 i - 1 3 j + 1 2 k )+ (3 i +2 j + k )

Step-by-step solution

The equation of line is aligned & 2 x+4=3 y+1=6 z-3 & 2(x+2)=3 (y+ 1 3 )=6 (z- 1 2 ) & x+2 1 2 = y+ 1 3 1 3 = z- 1 2 1 6 & x+2 3 = y+ 1 3 2 = z- 1 2 1 aligned The given line passes through (-2,- 1 3 , 1 2 ) and has direction ratios proportional to 3,2,1 . Vector equation of the line is r = (-2 i - 1 3 j + 1 2 k )+ (3 i +2 j + k )

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