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.

Rate this question :

Find the sum of tMathematics - Board Papers

Prove that in anyMathematics - Exemplar

Find the sum of tMathematics - Board Papers

Find a unit vectoMathematics - Board Papers

Write a unit vectMathematics - Board Papers

Find the positionMathematics - Board Papers

Write a unit vectMathematics - Board Papers

If <Mathematics - Board Papers

Write the positioMathematics - Board Papers

Find the sum of tMathematics - Board Papers