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The equilibrant of a force is the force which is equal and opposite to that force. If two forces are equal and opposite,
their x and y components are also equal, but the x and y components of the force are opposite in sign to those of the
equilibrant.

The x and y components of the a force are 2 Newtons and 3 Newtons repectively.
 

• What angle does the force make as measured counterclockwise from the positive x axis?

answer/question/discussion:

The force has magnitude F = sqrt( F_x^2 + F_y^2) = sqrt((2 N)^2 + (3 N)^2) = sqrt(13 N), or about 3.6 N.

The angle made by the force is theta = arcTan(F_y / F_x) = arcTan(3 N / (2 N) ) = arcTan (3/2) = 56 deg, approx.

What are the components of the equilibrant force?

The components of the equilibrant force are equal and opposite to the components of the force, so

• the x component of the equilibrant is -2 N and

• the y component of the equilibrant is -3 N.

What angle does the equilibrant force make as measured counterclockwise from the positive x axis? 

The rule for the angle:

• the angle is arcTan(y comp / x comp), plus 180 deg if the x component is negative.

For the present example we have

• angle = arcTan(-3 N / (-2 N) ) + 180 deg = 56 deg + 180 deg = 236 deg, approx..

Note that the original vector is in the first quadrant (its angle is about 56 deg), and the equilibrant is in the third quadrant (at the 236 deg angle), with the two vectors being equal and opposite.

The figures below depict the original vector, the equilibrant and the two vectors acting together.  Each vector is depicted with its initial point at the origin.