1
Question
ABCDEF be a regular hexagon, and ¯¯¯¯¯¯¯¯AB=¯¯¯a, ¯¯¯¯¯¯¯¯BC=¯¯b then ¯¯¯¯¯¯¯¯¯AD+¯¯¯¯¯¯¯¯EB+¯¯¯¯¯¯¯¯FC=
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Solution
The correct option is B 4¯¯¯a
−−→AD=−−→AB+−−→BC+−−→CD
−−→EB=−−→ED+−−→DC+−−→CB
−−→FC=−−→FE+−−→ED+−−→DC
−−→AD+−−→EB+−−→FC=−−→AB+−−→ED+−−→FE+−−→ED+−−→DC
=a+2a+−−→FE+−−→DC
=3a+b+a−b (−−→FE=−−→BC −−→FE||−−→BC)
=4¯¯¯a
−−→AD=−−→AB+−−→BC+−−→CD
−−→EB=−−→ED+−−→DC+−−→CB
−−→FC=−−→FE+−−→ED+−−→DC
−−→AD+−−→EB+−−→FC=−−→AB+−−→ED+−−→FE+−−→ED+−−→DC
=a+2a+−−→FE+−−→DC
=3a+b+a−b (−−→FE=−−→BC −−→FE||−−→BC)
=4¯¯¯a
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