Question
If a,b represent −−→AB,−−→BC respectively of a regular hexagon ABCDEF then −−→CD,−−→DE,−−→EF,−−→FA are
Answer: Option A
:
A
ABCDEF is a regular hexagon
⇒⃗AD=2⃗BC,⃗ED=⃗AB,⃗FE=⃗BC,⃗FA=⃗DC
Given ⃗AB=a,⃗BC=b
Now ⃗AB+⃗BC+⃗CD=⃗AD⇒a+b+⃗CD=2⃗BC
⇒⃗CD=2b−(a+b)=b−a⃗DE=⃗BA=−⃗AB=−a,⃗EF=⃗CB=−⃗BC=−b⃗FA=⃗DC=−⃗CD=−(b−a)=a−b
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:
A
ABCDEF is a regular hexagon
⇒⃗AD=2⃗BC,⃗ED=⃗AB,⃗FE=⃗BC,⃗FA=⃗DC
Given ⃗AB=a,⃗BC=b
Now ⃗AB+⃗BC+⃗CD=⃗AD⇒a+b+⃗CD=2⃗BC
⇒⃗CD=2b−(a+b)=b−a⃗DE=⃗BA=−⃗AB=−a,⃗EF=⃗CB=−⃗BC=−b⃗FA=⃗DC=−⃗CD=−(b−a)=a−b
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