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Question 1187455: A figure shows two forces acting at right angles on an object. They have magnitudes = 6.3 N and = 2.1 N. What third force will cause the object to be in equilibrium (acceleration equals zero)?
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! I do not know what your figure looks like, but it should be similar to one of the sketches below. You may have to rotate the figure, or flip it.
My teachers represented forces acting on the same object as arrows coming out of the same point, and they would represent the resultant (sum of) two forces as an arrow that would span the diagonal of the parallelogram (rectangle in this case) determined by the two forces. I expect that to be what a physics teacher would do. In that case, just look at the first sketch.
Maybe your teacher is a math teaches, and likes to represent sum of vectors by connecting the vectors tail to head. In that way of representing vectors, if you need a "third force will cause the object to be in equilibrium" it would be represented by the arrow that closes the triangle. In that case, look at the second sketch.
 or 
For the first sketch, you find the magnitude of the resultant of the two forces,
the  force, as the diagonal of the rectangle.
That is the hypotenuse of the congruent right triangles divides the rectangle into.
The Pythagorean theorem says that we can calculate that as
 for an exact (math class) answer, or
 or maybe just 
You can get the measure of angle  from
 --> 
The third force needed to "cause the object to be in equilibrium" is  , with the same magnitude as , but in the opposite direction.
It froms with the  force an angle measuring
 , indicated by a red arc in the first sketch.
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