Q. 85.0( 4 Votes )

Prove that the su

Answer :

Given: a regular octagon


To prove the sum of all vectors drawn from the centre of a regular octagon to its vertices is the zero vector


Proof:


Let O be the centre of a regular octagon, we know that the centre of a regular octagon bisects all the diagonals passing through it as shown in figure below







Thus,



The sum of all vectors drawn from the centre of a regular octagon to its vertices is



Substitute the values from eqn(i) in above eqn, we get





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


Hence, proved.


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