# Using the condition of vector equilibrium

• ritwik06
In summary, ritwik06 explained that the sigma is a symbol for summation and that if n equal vectors are at an angle their resultant is zero. He then offered a hint for how to solve a problem involving sigma. Finally, he explained that the sum of the components of the vectors will be zero.

## Homework Statement

Using the condition of vector equilibrium, prove that
$$\sum$$$$^{2n-1}_{k=0}$$ cos ((k*pi)/n)

Where n is an integer.

## Homework Equations

I know that if n equal vectors are at an angle (2*pi)/n
Their resultant is zero.

## The Attempt at a Solution

Please first explain to me what does this sigma signify and what is meant by its subscript and superscript. Then please give me an idea of what to do with this problem. Thanks.

Ritwik

The sigma is a symbol for summation. For example

$$\sum_{i = 1}^{i = 5} f(i)$$

just means $$f(1) + f(2) + f(3) + f(4) + f(5)$$. The subscript is the value at which i begins, and the superscript is the value at which i ends.

ritwik06 said:
I know that if n equal vectors are at an angle (2*pi)/n
Their resultant is zero.

HI ritwik06! Hint: Draw those n equal vectors.

What are the coordinates of their endpoints? Using the condition of vector equilibrium, prove that:

$$\sum_{k = 0}^{2n-1} cos \frac{k*pi}{n}=0$$
where n is an integer

Hey, help me please. Please tell me what do I have to prove.

Last edited:
Think about the components of the vectors you mentioned in your first post. What are the components, and what should their sum be?

ritwik06 said:

What do you mean its not applicable? All I did was show you what sigma meant, because you asked.

Precaution:
cos is upon the whole fraction {(k*pi)/n}
Please just let me know once what I need to prove. As u said dx that the superscript signifis the upperlimit of the variable. but in this case the limit itself is a variable. Please help

dx said:
Think about the components of the vectors you mentioned in your first post. What are the components, and what should their sum be?

What do you mean its not applicable? All I did was show you what sigma meant, because you asked.

Thir sum will be zero!

Oh, yes but please re chck the format of my question. Please!

No, its not. n is the number of vectors. Its not changing.

ritwik06 said:
Thir sum will be zero!

Ok, so write it out explicitly and see what its going to look like.