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newmoon newmoon
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10 years ago
determine the resultant of three vectors having magnitude of 1,2, and 3 forming sides of an equilateral triangle.
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10 years ago
Hi, is the triangle labelled? If it is labeled ABC, what are the magnitudes between AB, BC, and CA?

Here's a similar question:

Question
ABC is an equilateral triangle. Forces 12N, 10N and 10N act along AB, BC and CA respectively. Find the magnitude and direction of the resultant force?

Answer
You haven't specified the direction of the applied forces. Does the 12N force act from A to B or from B to A, for example.

With the following assumptions:

A:(x,y) = (0,0)
B:(x,y) = (rcos60, rsin60)
C:(x,y) = (r, 0)

Ignoring moments, forces act at a common point, with directions from A to B, from B to C, and from C to A:
Fab = 12cos60x + 12sin60y
Fbc = 10cos60x - 10sin60y
Fca = -10x

F = (22cos60 - 10)x + (2sin60)y

Direction of F: Θ = arctan[sin60/(11cos60-5)] = arctan(1.73205) = 60°
Magnitude of F: |F| = SQTR( [(22cos60-10)² + 4sin²60] ) = 2
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