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AP EAMCET20228 Jul 2022Morning ShiftMathematicsVector AlgebraActual

If e₁ , e₂ are two non-collinear unit vectors such that | e ₁+ e ₂ |= 3 then (2 e ₁-5 e ₂ ), (3 e ₁+ e ₂ )=

Options

  1. A11 2
  2. B-11 2
  3. C9 2
  4. D-9 2

Correct answer

B. -11 2

Step-by-step solution

Given e ₁ & e ₂ are units vectors, then | e _ i |=1= | e ₂ | Now, | e _ i + e ₂ |= 3 aligned & | e _ i + e ₂ |^2=3 & ( e ₁ + e ₂ ) ( e ₁ + e ₂ )=3 & e ₁ e ₁ + e ₁ e ₂ + e ₂ e ₁ + e ₂ e ₂ =3 & | e ₁ |^2+ | e ₂ |^2+2 e ₂ e ₁ =3 & 1+1+2 e ₂ e ₁ =3 & 2 e ₂ e ₁ =1 aligned e ₂ e ₁ = 1 2 ...(i) (2 e ₁ -5 e ₂ ) (3 e ₁ + e ₂ )=6 | e ₁ |^2+2 e ₁ e ₂ -1-5 | e ₂ |^2 Now, aligned & 6 1+13 1 2 -5 1 & 1- 13 2 = -11 2 aligned

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