Prove that the sum of all vectors drawn from the centre of a regular octagon to its vertices is the zero vector.

Explanation

Let O be the center of octagon with vertices A B C D E F G H

Since ,{O} is the mid-point,

` vec{ {AO}}=- vec{ {OE}}`

`{AO}+ {OE}=0 quad ldots(1) `

Similarly,

`vec{ {BO}}+ vec{ {OF}}=0 `

`{CO}+ {OG}=0 quad ldots(3) `

` {DO}+ {OH}=0 `

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