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KCET2008MathematicsVector 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 Now, a b = | array ccc i & j & k 1 & 1 & 0 0 & 1 & 1 array |= i (1-0)- j (1-0)+ k (1-0)= i - j + k and | a b |= 1²+(-1)²+1² = 3 Required unit vector = a b a b = i - j + k 3

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