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JEE Main20254 Apr 2025Morning ShiftMathematicsVector AlgebraActual

Consider two vectors u =3 i - j and v =2 i + j - k , 0 . The angle between them is given by ⁻¹ ( 5 2 7 ) . Let v = v ₁+ v ₂ , where v ₁ is parallel to u and v ₂ is perpendicular to u . Then the value | v ₁ |^2+ | v ₂ |^2 is equal to

Options

  1. A23 2
  2. B14
  3. C25 2
  4. D10

Correct answer

B. 14

Step-by-step solution

aligned & u =3 i - j , v =2 i + j - k , & u v | u | v | = & 5 10 5+ ^2 = 5 2 7 & ^2=9 =3( 0) & v = v ₁+ v ₂ & | v |^2= v ₁^2+ v ₂^2+2 v ₁ v ₂ & 14= v ₁^2+ v ₂^2+0 ( v ₁ v ₂ ) & | v ₁^2 |+ | v ₂^2 |=14 aligned

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