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MHT CET202120 Sep 2021Evening ShiftMathematicsThree Dimensional GeometryActual

The vector equation of the lien whose Cartesian equations are y=2 and 4 x-3 z+5=0 is

Options

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

Correct answer

B. r = (2 j + 5 3 k )+ (3 i +4 k )

Step-by-step solution

We have lines y-2=0 and 4 x-3 z+5=0 aligned & 4 x=3 z-5=3 [z- ( 5 3 ) ] & 4 x 12 = 3 [z- ( 5 3 ) ] 12 x 3 = z- ( 5 3 ) 4 , y=2 aligned Thus line passes through the point (0,2, 5 3 ) i.e. a point having position vector 2 j + 5 3 k Also direction ratios of a line are 3,0,4 Hence required vector equation is r = (2 j + 5 3 k )+ (3 i +4 k )

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