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Question
If Five forces →AB,→AC,→AD,→AE,→AF act at the vertex A of a regular hexagon ABCDEF, then their resultant is? (where O is the centroid of the hexagon)
If Five forces →AB,→AC,→AD,→AE,→AF act at the vertex A of a regular hexagon ABCDEF, then their resultant is? (where O is the centroid of the hexagon)
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Solution
The correct option is A 2→AO
−−→AB+−−→AC+−−→AD+−−→AE+−−→AF AS ABCDEF is a regular hexagon −−→CD∥−−→AF=|−−→CD|=|−−→AF|
From triangle law of addition −−→AC+−−→CD=−−→AD−−→AC+−−→AF=−−→AD−−→AB+(−−→AC+−−→AF)+−−→AD+−−→AE−−→AB+−−→AD+−−→AD+−−→AE2−−→AD+−−→AB+−−→AE
Also, |−−→AB|=|−−→ED|−−→AB||−−→ED⇒−−→AB+−−→AE=−−→ED+−−→AE=−−→AD⇒2−−→AD+−−→AD=3−−→AD0 is the center and also midpoint of −−→ADOA=0D−−→AD=2−−→AO⇒3−−→AD=6−−→AO Hence, (D) is the correct option
−−→AB+−−→AC+−−→AD+−−→AE+−−→AF AS ABCDEF is a regular hexagon −−→CD∥−−→AF=|−−→CD|=|−−→AF|
From triangle law of addition −−→AC+−−→CD=−−→AD−−→AC+−−→AF=−−→AD−−→AB+(−−→AC+−−→AF)+−−→AD+−−→AE−−→AB+−−→AD+−−→AD+−−→AE2−−→AD+−−→AB+−−→AE
Also, |−−→AB|=|−−→ED|−−→AB||−−→ED⇒−−→AB+−−→AE=−−→ED+−−→AE=−−→AD⇒2−−→AD+−−→AD=3−−→AD0 is the center and also midpoint of −−→ADOA=0D−−→AD=2−−→AO⇒3−−→AD=6−−→AO Hence, (D) is the correct option
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