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MHT CET20242 May 2024Morning ShiftMathematicsVector AlgebraActual

If the vectors a = i - j +2 k , b =2 i +4 j + k and c = mi + j + nk are mutually perpendicular, then ( m , n ) is

Options

  1. A(3,-2)
  2. B(-2,3)
  3. C(2,-3)
  4. D(-3,2)

Correct answer

D. (-3,2)

Step-by-step solution

a = i - j +2 k , ~b =2 i +4 j + k and c =m i + j + n k a and c are orthogonal aligned & a c =0 & ~m (1)+(1)(-1)+ n (2)=0 & m-1+2 n =0 & m+2 n=1...(i) aligned Also, b and c are orthogonal array ll & b c =0 & 2( ~m )+4(1)+ n (1)=0 & 2 ~m + n =-4...(ii) array Solving (i) and (ii), we get array ll & m=-3, n =2 & ( ~m , n )=(-3,2) array

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