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COMEDK2014MathematicsVector Algebra

Find , if is the angle between the vectors 3 i + j +2 k and i + j +2 k .

Options

  1. A5 21
  2. B5 21
  3. C4 21
  4. D3 21

Correct answer

A. 5 21

Step-by-step solution

Let a =3 i + j +2 k and b = i + j +2 k gathered a b = | array lll i & j & k 3 & 1 & 2 1 & 1 & 2 array | = i (2-2)- j (6-2)+ k (3-1)=-4 j +2 k gathered | a b |= (-4)²+(2)² = 16+4 = 20 Since, | a b |=| a || b | , If is angle between a and b . aligned 20 &= 9+1+4 1+1+4 &= 20 6 14 &= 20 6 14 = 5 21 aligned

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