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NDA2015MathematicsVector AlgebraActual

If | a |=7,| b |=11 and | a + b |=10 3 , then | a - b | is equal to

Options

  1. A40
  2. B10
  3. C4 10
  4. D2 10

Correct answer

D. 2 10

Step-by-step solution

| a |=7,| ~b |=11 and | a + b |=10 3 Now | a + b |^2=| a |^2+| b |^2+2| a || b | array ll & (10 3 )^2=49+121+2 7 7 & 300=170+154 & 300-170 154 = & 65 77 = array aligned & Now, | a - b |^2=| a |^2+| b |^2-2| a || b | & =(7)^2+(11)^2-2 7 11 65 77 & =49+121-2 65 & =170-130=40 & | a - b |= 40 =2 10 aligned Option (D) is correct.

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