Question

How many minimum numbers of non-zero vectors in different planes can be added to give zero resultant?

• A. $2$
• B. $3$
• C. $4$
• D. $5$

Answer 1

The correct option is C

$4$

Explanation of the correct option :

If the vectors are in different planes, they would need to cancel components in at least $3$ dimensions to make the resultant $0$.

Therefore, we would need at least $4$ vectors such that $3$ of them when added cancel their components in a plane and add to get a single vector perpendicular to this plane. The fourth vector would nullify this perpendicular vector.

For Example, suppose $A,B,C,$ and $D$ are four vectors and no three of them are coplanar. if the result of $A$and $B$ be $X$, and the resultant of $C$ and $D$ be $Y$. if $X$ and $Y$be equal in magnitude but in opposing directions, that's the only way the resultant of $A,B,C,D$ be zero, without any three of them being in the same plane.

Hence the correct option is C.