Calculus

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.

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  1. 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-1x.
    Note that if x<0, then A>90°.

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