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Let the vectors a → ,   b → and c → are perpendicular to b → + c → ,   c → + a → and a → + b → respectively. If a → + b → = 6 , | b → + c → | = 8 and c → + a → = 10 , then the value of | a → + b → + c → | is equal to

Options

  1. A5 5
  2. B50
  3. C10 2
  4. D10

Correct answer

D. 10

Step-by-step solution

Since, a → ⋅ b → + c → = 0 ⟹ a → ⋅ b → + a → ⋅ c → = 0 Similarly, b → ⋅ c → + b → ⋅ a → = 0 &   c → ⋅ a → + c → ⋅ b → = 0 ∴   a → ⋅ b → + a → ⋅ c → + b → ⋅ c → = 0 ...(i) Given, | a → + b → | = 6 ⟹ | a → | 2 + | b → | 2 + 2 a → ⋅ b → = 36 ....(ii) Similarly,

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