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Let a → = 3 ,   b → = 4 ,   c → = 5 and a → × a → × c → + 4 b → = 0 , then the value of a → × c → 2 equals to

Options

  1. A9 256
  2. B16 3
  3. C256 9
  4. D3 16

Correct answer

C. 256 9

Step-by-step solution

a → × a → × c → = - 4 b → ⇒ a → ⋅ c → a → - a → ⋅ a → c → = - 4 b → Let, a → ⋅ c → = a → c → cos θ ⇒ 15 cos ⁡ θ a → - 9 c → = - 4 b → ⇒ 15 cos ⁡ θ a → - 9 c → 2 = 16 b → 2 ⇒ 225 c o s 2 θ × 9 + 81 × 25 - 270 × 15 c o s 2 θ = 16 × 1 6 ⇒ 2025 c o s 2 θ = 176 9 ⇒ c o s 2

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