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Let q → and r → be non-collinear vectors. If p → is a vector such that p → . q → + r → = 4 and p → × q → × r → = x 2 - 2 x + 6 q → + sin ⁡ y r → , then x , y lies on the line

Options

  1. Ax + y = 0
  2. Bx - y = 0
  3. Cx = 1
  4. Dy = π

Correct answer

C. x = 1

Step-by-step solution

p → . r → q → - p → . q → r → = x 2 - 2 x + 6 q → + sin ⁡ y r → on comparison, we get, p → . r → = x 2 - 2 x + 6 and - p → . q → = sin ⁡ y ∵   p → . q → + p → . r → = 4 (given) ⇒ x 2 - 2 x + 6 - sin ⁡ y = 4 ⇒ x - 1 2 + 1 = sin ⁡ y ∵   x - 1 2 + 1 ≥ 1 ,     sin ⁡ y ≤ 1 ∴ Both sides are equal for x = 1 ,   sin ⁡ y = 1

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