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Let x → and y → are 2 non-zero and non-collinear vectors, then the largest value of k such that the non-zero vectors k 2 - 5 k + 6 x → + k - 3 y → and 2 x → + 5 y → are collinear is

Options

  1. A3
  2. B6
  3. C12 5
  4. D- 1

Correct answer

C. 12 5

Step-by-step solution

Let, a → = k 2 - 5 k + 6 x → + k - 3 y → and b → = 2 x → + 5 y → ∵ a → and b → are collinear vectors ⇒ k 2 - 5 k + 6 2 = k - 3 5 ⇒ k = 3 , 12 5 But, for k = 3 , a → = 0 (not possible)

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