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Let a → = 2 i ^ + 3 j ^ + 4 k ^ , b → = i ^ - 2 j ^ + k ^ and c → = i ^ + j ^ - k ^ . If r → × a → = b → and r → ⋅ c → = 3 , then the value of r → is equal to

Options

  1. A155
  2. B17
  3. C2 17
  4. D3

Correct answer

A. 155

Step-by-step solution

Given, r → × a → = b → Taking right cross product with c → , we get, r → × a → × c → = b → × c → ⇒ r → ⋅ c → a → - a → ⋅ c → r → = b → × c → ⇒ 3 a → - r → = b → × c → ⇒ r → = 3 2 i ^ + 3 j ^ + 4 k ^ - i ^ + 2 j ^ + 3 k ^ ⇒ r → = 5 i ^ + 7 j ^ + 9 k ^ ⇒ r → = 155

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