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AP EAMCET201822 Apr 2018Evening ShiftMathematicsVector AlgebraActual

Let m be the unit vector orthogonal to the vector i - j + k and coplanar with the vectors 2 i + j and j - k . If a = i - k , then the length of the perpendicular from the origin to the plane r m = a m is

Options

  1. A1 26
  2. B1 5
  3. C5 26
  4. D1

Correct answer

C. 5 26

Step-by-step solution

The vector m is coplane with (2 i + j ) and ( j - k ) So, aligned & m =x(2 i + j )+y( j - k ) & m =2 x i +(x+y) j -y k aligned m is orthogonal to the vector i - j + k , so 2 x-(x+y)-y=0 array lrl & | m |=1 4 x^2+(x+y)^2+y^2=1 & 16 y^2+9 y^2+y^2=1 & 26 y^2=1 y= 1 26 . array So, x= 2 26 m = ( 4 26 i + 3 26 j - 1 26 k ) The length of the perpendicular from the origin to the plane r . m = a m is So, aligned & m |=| i - k ) [ 4 26 i + 3 26 j - 1 26 k ] & = 4 26 + 1 26 = 5 26 units. aligned

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