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99 Percentile Qs Bank for JEE MainMathematicsVector Algebra

The set of values of c for which the angle between the vectors c x i ^ - 6 j ^ + 3 k ^ and x i ^ - 2 j ^ + 2 c x k ^ is acute for every x ∈ R is

Options

  1. A0 , 4 3
  2. B0 , 4 3
  3. C11 9 , 4 3
  4. D0 , 4 3

Correct answer

D. 0 , 4 3

Step-by-step solution

If two vectors are included with an acute angle then a → . b → > 0 ⇒ c x 2 + 12 + 6 c x > 0 c > 0   a n d   ∆ < 0 ⇒ 36 c 2 - 48 c < 0 ⇒ c 3 c - 4 < 0 ⇒ c ∈ 0 , 4 3

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