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MHT CET202410 May 2024Evening ShiftMathematicsVector AlgebraActual

The vector of magnitude 6 units and perpendicular to vectors 2 i + j -3 k and i -2 j + k is

Options

  1. A2 3 (- i + j + k )
  2. B2 3 ( i - j + k )
  3. C2 3 ( i + j + k )
  4. D2 3 (- i - j + k )

Correct answer

C. 2 3 ( i + j + k )

Step-by-step solution

Let the required vector be r =x i +y j +z k . Then, | r |=6 x^2+y^2+z^2=36 Now, r is perpendicular to vectors a =2 i + j -3 k and b = i -2 j + k . array ll & a b = | array ccc i & j & k 2 & 1 & -3 1 & -2 & 1 array |=-5( i + j + k ) & x=y= z & Let x=y= z = array Let x=y=z= . From (i), we get array ll & 3 ^2=36 & =2 3 array Required vector is 2 3 ( i + j + k )

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