What is the minimum number of non-zero vector | vedclass

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(C) To obtain a zero resultant,the vectors must form a closed polygon. If vectors are in the same plane,the minimum number of vectors required is $3$

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$4$

Vedclass · Answer

(C) To obtain a zero resultant,the vectors must form a closed polygon. If vectors are in the same plane,the minimum number of vectors required is $3$ (forming a triangle). However,the question specifies that the vectors are in different planes. If we have $3$ vectors in different planes,their resultant cannot be zero because the resultant of any two vectors lies in the plane containing them,and the third vector (being in a different plane) cannot cancel this resultant. Therefore,we need at least $4$ vectors. For example,consider a tetrahedron where the four vectors represent the four faces; their sum is zero. Thus,the minimum number of non-zero vectors in different planes required to give a zero resultant is $4$.

What is the minimum number of non-zero vectors in different planes that can be added to give a zero resultant?

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