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  4. Five forces A B, A C, A D, A E, A F act at the vertex A of a regular hexagon A B C D E F. If O is the centroid of the hexagon, then their resultant is a force given by

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Q. Five forces $A B, A C, A D, A E, A F$ act at the vertex $A$ of a regular hexagon $A B C D E F$. If $O$ is the centroid of the hexagon, then their resultant is a force given by

Vector Algebra

Solution:

If $R$ is the resultant of given forces, then
image
$ R =A B+A C+A D+A E+A F $
$=E D+A C+A D+A E+C D $
$(\because A B=E D $ and $A F=C D) $
$=(A C+C D)+(A E+E D)+A D$
$=A D+A D+A D=3 A D=6 A O$