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COMEDK2019MathematicsVector Algebra

A unit vector perpendicular to both the vectors i + j and j + k is

Options

  1. A- i - j + k 3
  2. Bi + j - k 3
  3. Ci + j + k 3
  4. Di - j + k 3

Correct answer

D. i - j + k 3

Step-by-step solution

Let a = i + j and b = j + k Then, unit vector perpendicular to both a and b is a b |a b| Now, a b = | array ccc i & j & k 1 & 1 & 0 0 & 1 & 1 array |= i - j + k and | a b |= (1)²+(-1)²+(1)² = 3 Thus, required vector = i - j + k 3

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