Question 3: The resultant of two forces, one is double than the other, is perpendicular to the smaller force. What is angle between two forces?

Answer

Let two forces and are acting with one another according to the conditions of the problem, i-e,

(1) The magnitude of  is double the magnitude of .

(2) The resultant of both forces is perpendicular to the smaller force, i-e, .

(3) These situations are shown in the diagram.

Now, to the right-angled triangle, apply the Pythagoras theorem,

So Θ = 60°

As the angle between two vectors is determined by putting them tail to tail, therefore, looking at the figure above and using geometry, the angle between the two forces must be 90 + 30 = 120 degrees.