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Question
ABCDE is a pentagon. Forces −−→AB,−−→AE,−−→DC,−−→ED act at a point. Which force should be added to this system to make the resultant 2−−→AC
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Solution
The correct option is C −−→BC
−−→AB+−−→AE+−−→DC+−−→ED=−−→AB+−−→DC+−−→AE+−−→ED=−−→AB+−−→DC+−−→AD=−−→AB+(→C−→D)+(→D−→A)=−−→AB+(→C−→A)=−−→AB+−−→AC
Now to make this resultant equal to 2−−→AC we need to add −−→BC
∴−−→AB+−−→BC+−−→AC
=−−→AC+−−→AC
=2−−→AC
Hence, −−→BC must be added to make the resultant 2−−→AC.
−−→AB+−−→AE+−−→DC+−−→ED=−−→AB+−−→DC+−−→AE+−−→ED=−−→AB+−−→DC+−−→AD=−−→AB+(→C−→D)+(→D−→A)=−−→AB+(→C−→A)=−−→AB+−−→AC
Now to make this resultant equal to 2−−→AC we need to add −−→BC
∴−−→AB+−−→BC+−−→AC
=−−→AC+−−→AC
=2−−→AC
Hence, −−→BC must be added to make the resultant 2−−→AC.
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