Calculus
posted by Ariza on .
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.

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+c²a²)/(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°.