The resultant of two forces acting on the same point is maximum when the forces are acting in the same direction and minimum when they operate in opposite direction.
When the two forces are acting in the same direction the angle between the direction to the two forces is 0. In this case the resultant force is sum of the two forces and its direction is same as the two independent forces.
In the question the magnitude of the two forces are given as 12 N and 5 N.
Therefor their net magnitude will be 12 + 5 = 17 N
When the two forces are acting in the opposite direction the angle between the direction to the two forces is 180 degrees. In this case the resultant force is the difference in the magnitude of two forces acting in the direction of larger of the two forces.
Thus when the forces with the given magnitude are acting in opposite direction their net magnitude will be:
12 - 5 = 7 N
This resultant force will act in the direction of the component force with magnitude of 12 N.
When the two forces are acting at right angles their magnitude is:
(12^2 + 5^2)^1/2 = (144 + 25)^1/2 = 169^1/2 = 13 N
This resultant force acts at an angle A with the greater of the two forces and towards the smaller force such that:
tanA = (Magnitude of smaller force)/Magnitude of greater force
= 5/12 = 0.41666
Measure of angle A corresponding to this value of tanA is 22.6 degrees.
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