What is the minimum number of coplanar vector | vedclass

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(B) For the sum of vectors to be zero,they must form a closed polygon when placed head-to-tail.If there are only $2$ vectors of different magnitudes,s

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$3$

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(B) For the sum of vectors to be zero,they must form a closed polygon when placed head-to-tail.If there are only $2$ vectors of different magnitudes,say $\vec{A}$ and $\vec{B}$,their sum $\vec{A} + \vec{B} = 0$ implies $\vec{A} = -\vec{B}$. This means they must have the same magnitude and opposite directions,which contradicts the condition that they have different magnitudes.If there are $3$ vectors of different magnitudes,they can form a triangle (a closed polygon) if the sum of the lengths of any two sides is greater than the third side. For example,vectors of magnitudes $3, 4,$ and $5$ can form a triangle and their sum can be zero.Therefore,the minimum number of coplanar vectors of different magnitudes required to have a zero resultant is $3$.

What is the minimum number of coplanar vectors of different magnitudes whose sum can be zero?

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