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JEE Main20198 Apr 2019Evening ShiftMathematicsVector AlgebraActual

Let a → = 3 i ^ + 2 j ^ + x k ^ and b → = i ^ - j ^ + k ^ , for some real x . Then the condition for a → × b → = r to follow

Options

  1. A0 < r ≤ 3 2
  2. Br ≥ 5 3 2
  3. C3 2 < r ≤ 3 3 2
  4. D3 3 2 < r < 5 3 2

Correct answer

B. r ≥ 5 3 2

Step-by-step solution

As, We know that a &#8594; &#215; b &#8594; = i ^ j ^ k ^ 3 2 x 1 - 1 1 = 2 + x i ^ + x - 3 j ^ - 5 k ^ a &#8594; &#215; b &#8594; = 4 + x 2 + 4 x + x 2 + 9 - 6 x + 25 = 2 x 2 - 2 x + 38 Therefore, we have &#8658; a &#8594; &#215; b &#8594; &#8805; 75 2 &#8658; a &#8594; &#215; b &#8594; &#8805; 5 3 2

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