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JEE Main2006MathematicsVector AlgebraActual

A B C is a triangle, right angled at A . The resultant of the forces acting along A B , A C with magnitudes 1 A B and 1 A C respectively is the force along A D , where D is the foot of the perpendicular from A onto BC . The magnitude of the resultant is

Options

  1. AA B^2+A C^2 (A B)^2(A C)^2
  2. B(A B)(A C) A B+A C
  3. C1 A B + 1 A C
  4. D1 AD

Correct answer

D. 1 AD

Step-by-step solution

Magnitude of resultant aligned & = ( 1 A B )^2+ ( 1 A C )^2 = A B^2+A C^2 A B A C & = B C A B A C = B C A D B C = 1 A D aligned

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