Posted by **Ariza** on Sunday, May 2, 2010 at 7:39pm.

A force of 200 N is resolved into two vector components of 150 N and 80 N. Are these rectangular vector components? Justify your response. If they are not, determine the directions of the components.

- Calculus -
**MathMate**, Sunday, May 2, 2010 at 7:52pm
The two components and the negative of the resultant form a set of forces in equilibrium, therefore these forces (vectors) form the side of a closed triangle.

The three lengths (sides) are known (200,150,80), thus the angle can be found by the cosine rule:

x=cos(A)=(b²+c²-a²)/(2bc)

If cos(A) equals zero, the forces are perpendicular to each other. If not, angle A is given by cos^{-1}x.

Note that if x<0, then A>90°.

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