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AP EAMCET2016MathematicsVector Algebra

If | a |=3,| b |=4 and the angle between a and b is 120^ , then |4 a +3 b | is equal to

Options

  1. A25
  2. B7
  3. C13
  4. D12

Correct answer

D. 12

Step-by-step solution

We have, |a|=3,|b|=4 aligned & |4 a+3 b|^2=(4 a+3 b)(4 a+3 b) & =16|a|^2+9|b|^2+24 a . b & =16|a|^2+9|b|^2+24|a| .|b| & =16(3)^2+9(4)^2+24 3 4 120^ & =16 9+9 16+24 12 ( -1 2 )=144 & So, |4 a+3 b|= 144 =12 aligned

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