Let α → = 1 a i ^ + 4 b j ^ + b k ^ and β → = b i ^ + a j ^ + 1 b k ^ ∀ a , b 0 , then the maximum value of 12 6 + α → ⋅ β → is

Question

Let α → = 1 a i ^ + 4 b j ^ + b k ^ and β → = b i ^ + a j ^ + 1 b k ^ ∀ a , b > 0 , then the maximum value of 12 6 + α → ⋅ β → is, 12 11, 2, 1, 10 9

MARKS App · Accepted Answer

α → ⋅ β → = b a + 4 a b + 1 ∵ b a + 4 a b ≥ 4 1 + b a + 4 a b ≥ 5 6 + α → ⋅ β → ≥ 11 ⇒ 6 + α → ⋅ β → 12 ≥ 11 12 ⇒ 12 6 + α → ⋅ β → ≤ 12 11