5
Question
If 2^i and ^j+√3^j are the vectors representing sides AB and BC respectively of a regular hexagon ABCDEF. Express vectors ¯¯¯¯¯¯¯¯¯CD,¯¯¯¯¯¯¯¯¯DE,¯¯¯¯¯¯¯¯FA,¯¯¯¯¯¯¯¯AC,¯¯¯¯¯¯¯¯¯AD,¯¯¯¯¯¯¯¯AE,¯¯¯¯¯¯¯¯CE
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Solution
The required vector of given sides are-−−−→AB=+−−→DE=−2ˆi
−−→AC=−−→AB+−−→BC
=2ˆi+(1+√3)ˆj
−−→BC+−−→DE=−−→CD
=−2ˆi+(1+√3)ˆj
−−→FA=−−→EF+−−→AB=−−−→BC+−−→AB=2ˆi−(1+√3)ˆj
−−→AD=−−→AC+−−→CD=2ˆi+(1+√3)ˆj+(−2ˆi)+(1+√3)ˆj=2(1+√3)ˆj
−−→AE=−−→AD+−−→DE=−2ˆi+(1+√3)ˆj
−−→CE=−−→CD+−−→DE=−2ˆi+(1+√3)ˆj−2ˆi+(1+√3)ˆJWhich is the required given answer.
−−−→AB=+−−→DE=−2ˆi
−−→AC=−−→AB+−−→BC
=2ˆi+(1+√3)ˆj
−−→BC+−−→DE=−−→CD
=−2ˆi+(1+√3)ˆj
−−→FA=−−→EF+−−→AB=−−−→BC+−−→AB=2ˆi−(1+√3)ˆj
−−→AD=−−→AC+−−→CD=2ˆi+(1+√3)ˆj+(−2ˆi)+(1+√3)ˆj=2(1+√3)ˆj
−−→AE=−−→AD+−−→DE=−2ˆi+(1+√3)ˆj
−−→CE=−−→CD+−−→DE=−2ˆi+(1+√3)ˆj−2ˆi+(1+√3)ˆJ
Which is the required given answer.
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