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a → ,   b → and c → are coplanar unit vectors. A unit vector d → is perpendicular to them. If a → × b → × c → × d → = 3 26 i ^ - 2 13 j ^ + 6 13 k ^ and the angle between a → and b → is 3 0 ∘ , then c → is equal to

Options

  1. A3 13 i ^ - 4 13 j ^ + 12 13 k ^
  2. B2 7 i ^ - 3 7 j ^ + 6 7 k ^
  3. C3 i ^ - 4 j ^ + 12 k ^
  4. D1 3 i ^ - 1 3 j ^ + 1 3 k ^

Correct answer

A. 3 13 i ^ - 4 13 j ^ + 12 13 k ^

Step-by-step solution

a → ⋅ d → = b → ⋅ d → = c → ⋅ d → = 0 (Given) a → = b → = c → = d → = 1           a → ⋅ b → = 3 2 a → × b → × c → × d → = 3 26 i ^ - 2 13 j ^ + 6 13 k ^ ⇒ a → × b → ⋅ d → c → - a → × b → ⋅ c → d → = 3 26 i ^ - 2 13 j ^ + 6 13 k ^ ... ( 1 ) ∵   a → ,   b →

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