Question

15 vectors each magnitude is 5 units are represented by the sides of aclosed polygon all taken in same order what will be their resultant ?

Answer 1

Given:

15 vectors each magnitude is 5 units are represented by the sides of a closed polygon all taken in same order.

To find:

Resultant of all the vectors.

Calculation:

First let's define Polygon Law of Vector Addition:

Polygon law of vector addition States that if a number of vectors are taken in order, the net summation of the vector will be represented by the closing side in the opposite direction.

Let closing side vector be R.

As per Polygon Law:

$\therefore \: \vec{R} = \vec{A_{1}} + \vec{A_{2}} + .... + \vec{A_{14}}$

$= > \vec{A_{1}} + \vec{A_{2}} + .... + \vec{A_{14}} - \vec{R} = 0$

$= > \: \sum \: ( \vec{A_{n}}) = 0$

Hence resultant of all the vectors is zero.

Trick:

• Whenever n number of vectors are taken in order to form a polygon the resultant vector will always be zero.