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AP EAMCET201825 Apr 2018Morning ShiftMathematicsVector AlgebraActual

If a → = 2 i ^ + j ^ - 3 k ^ , b → = i ^ - 2 j ^ + k ^ , c → = - i ^ + j ^ - 4 k ^ and d ¯ = i ^ + j ^ + k ^ , then | a → × b → × c → × d → | =

Options

  1. A5 114
  2. B5 94
  3. C5 124
  4. D5 78

Correct answer

D. 5 78

Step-by-step solution

Given a → = 2 i ^ + j ^ - 3 k ^ b → = i ^ - 2 j ^ + k ^ c → = - i ^ + j ^ - 4 k ^ d ¯ = i ^ + j ^ + k ^ Now, a → × b → = i ^ j ^ k ^ 2 1 - 3 1 - 2 1 = - 5 i ^ - 5 j ^ - 5 k ^ c → × d → = i ^ j ^ k ^ - 1 1 - 4 1 1 1 = 5 i ^ + 3 j ^ - 2 k ^ Now, a → × b → × c → × d → = i ^ j ^ k ^ - 5 - 5 - 5 5 3 - 2 = 25 i ^ - 35 j ^ + 10 k ^ a → × b → × c → × d → = 625 + 1225 + 100 = 1950 = 5 78

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