Question

two forces each of magnitude f acts perpendicular to each other . the angle made by resultant force with horizontal will be​

Answer 1

Actually, the “perpendicular” vectors should be called “orthogonal” vectors. (The proper term when talking about “perpendicular” vectors)

To find the angle between the result vector and the horizontal, we can assign some variables. Let f be the magnitude of the vector and let h,l be the y and x component of the vector, respectively.

We can find the angle using the arcsin function.

We know that the total y-component will just be h

The total length of the result vector would be:

sqrtf2+h2+l2 , but we know that h2+l2=f2

So, the angle will be equal to:

arcsin(h/(f∗sqrt2))