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KVPY2015MathematicsVector Algebra

Let a =6 i -3 j -6 k and d = i + j + k . Suppose that a = b + c where b is parallel to d and c is perpendicular to d . Then c is

Options

  1. A5 i -4 j - k
  2. B7 i -2 j -5 k
  3. C4 i -5 j + k
  4. D3 i +6 j -9 k

Correct answer

B. 7 i -2 j -5 k

Step-by-step solution

a =6 i -3 j -6 k d = i + j + k a = b + c b = d & c d =0 b = i + j + k From (1)6 i -3 j -6 k = i + j + k + c c =(6- ) i -(3+ ) j -(6+ ) k c d =0 =-1 c =7 i -2 j -5 k

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