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JEE Main202229 Jun 2022Evening ShiftMathematicsVector AlgebraActual

Let A , B , C be three points whose position vectors respectively are: a → = i ^ + 4 j ^ + 3 k ^ b → = 2 i ^ + α j ^ + 4 k ^ , α ∈ R c → = 3 i ^ - 2 j ^ + 5 k ^ If α is the smallest positive integer for which a → , b → , c → are non-collinear, then the length of the median, △ A B C , through A is:

Options

  1. A82 2
  2. B62 2
  3. C69 2
  4. D66 2

Correct answer

A. 82 2

Step-by-step solution

Let us assume that vectors are collinear so, A B → ∥ A C → if 1 2 = α - 4 - 6 = 1 2 ⇒ α = 1 Now, for a → ,   b → ,   c → to be non-collinear smallest positive integer will be α = 2 So, mid-point of B C = M 5 2 ,   0 ,   9 2 Now, A M = 9 4 + 16 + 9 4 = 82 2

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