Resultant of 3 vectors along the sides of an equilateral triangle

[cr7einstein]

Homework Statement

Hi all,

It is a homework problem, but I really don't quite understand the question. It reads-

"3 forces of magnitudes 10N, 20N, and 30N acting on a point are parallel to the sides of an equilateral triangle, taken in order. Find their resultant"

Homework Equations

The Attempt at a Solution

What I think is, as the resultant of 3 vectors forming a closed figure is 0, the answer should be 0.But the answer is given as $$10 \sqrt{3}$$. How?

Thanks in advance! (PS- Please add a diagram, if possible)

 

[Dr. Courtney]

Steps in adding vectors:

Draw a picture

Compute x and y components of each vector

Add x components to get x component of sum

Add y components to get y component of sum

If needed, put resultant back into magnitude angle form with Pythagoras and atan

 

[cr7einstein]

Thanks.
The problem is I don't know how to draw the diagram, and why should the resultant not be zero? It does form a closed figure, doesn't it?

 

[cr7einstein]

Also, aren't there 3 vectors? SO, am I supposed to take one of them along the X axis?

 

[Dr. Courtney]

The resultant would only be zero if all three forces had the same magnitude.

Draw F1 along the x axis.
Draw F2 with a 120 deg angle wrt the +x axis.
Draw F3 with a 210 deg angle wrt the +x axis.

 

[CWatters]

+1 to that.

Note the question says the vectors are parallel to the sides of an equilateral triangle not that they are arranged in a triangle.

 

[haruspex]

What I think is, as the resultant of 3 vectors forming a closed figure is 0

You are confusing two concepts. If you take the forces acting at a point and draw them as a chain in which:

• The head end of one touches the tail of the next
• Each line is parallel to the force it represents
• The length of each line is proportional to the magnitude of the force

then the line from the tail of the first in the chain to the head of the last in the chain represents the resultant. In particular, if it forms a closed polygon then the resultant is zero.
But the equilateral triangle here does not represent the force magnitudes. It is only telling you the directions of the forces. If you try to draw a triangle in which all the angles are 60 degrees but you make the lines different lengths then it won't close.