→a and →b form the consecutive sides of a regular hexagon ABCDEF. →AB=→a,→BC=→b
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Solution
→AB=→a,→BC=→b →AC=→AB+→BC=→a+→a (i) →AD=2→BC=2→b (ii) (because AD is parallel to BC and twice its length). →CD=→AD−→AC=2→b−(→a+→b)=→b−→a →FA=−→CD=→a−→b (iii) →DE=−→AB=−→a (iv) →EF=−→BC=−→b (v) →AE=→AD+→DE=2→b−→a (vi) →CE=→CD+→DE=→b−→A−→A=→b−2→a (vii)