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MHT CET202210 Aug 2022Evening ShiftMathematicsVector AlgebraActual

Let a =3 i +2 j +x k and b = i - j + k , for some real x . Then | a b |=r is possible, if

Options

  1. A0
  2. Br 5 3 2
  3. C3 3 2
  4. D3 2 r 3 3 2

Correct answer

B. r 5 3 2

Step-by-step solution

aligned & a b = | array ccc i & j & k 3 & 2 & x 1 & -1 & 1 array |=(2+x) i +(x-3) j +(-3-2) k & now r=| a b |= (2+x)^2+(x-3)^2+(-5)^2 & = 2 x^2-2 x+38 & = 2 (x- 1 2 )^2+ 75 2 & r_ = 75 2 at x= 1 2 & r 5 3 2 aligned

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