Question

The resultant of two forces of magnitudes 4n and 4√2n makes angle 90degrees with smaller force .find the angle between two vectors

Answer 1

Given :

Force 1 (F₁) = 4n

Force 2 (F₂) = 4√2 n

Angle between resultant and F₁ = 90°

To Find :

The angle between the vectors

Solution :

• From the diagram given below it is a right angle triangle.By applying pythagoras theorem

         R² + (4n)² = (4√2n)²

         R² + 16n² = 32n²

         R² = 16n²

         R = 4n

• The resultant of two forces is given by

          R = √F₁²+F₂²+2F₁F₂Cosθ

          16n² = 16n² + 32n² + 16√2n² Cosθ

          32n² + 16√2n² Cosθ = 0

          Cosθ = -(1/√2)

          θ = 135°

 The angle between two vectors is 135°