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  4. There are N coplanar vectors each of magnitude V. Each vector is inclined to the preceding vector at angle 2 π / N. What is the magnitude of their resultant?

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Q. There are $N$ coplanar vectors each of magnitude $V$. Each vector is inclined to the preceding vector at angle $2 \pi / N$. What is the magnitude of their resultant?

AIIMSAIIMS 2009

Solution:

Since each of $N$-coplanar vector is inclined at $2 \pi / N$ to the preceding hence, they will from a closed polygen. Therefore, their resultant must be zero.