Question

three vectors of equal magnitude are acting on the three sides of an equilateral triangle . the magnitude of their resultant is :-

Answer 1

since they act along equilateral triangle, when you join them head to tail, you can see that they go back to starting point.
therefore, resultant = 0

Answer 2

As-salamu-alaykum!

we know that according to polygon law of addition that if a number of vectors are represented in magnitude and direction by the sides of the polygon taken in same order, then their resultant is represented in magnitude and direction by the closing side of the polygon taken in the opposite order.

In case of regular polygon (all sides and angles between adjacent sides are equal), the resultant is that vector having the same magnitude as any one of the remaining vectors and is represented by the closing side of the polygon taken in the opposite order.

let us move on to the question now :

As Equilateral triangle is a regular polygon : if two vectors of equal magnitude represent the sides of equilateral triangle, then resultant of these two vectors is equal to the magnitude of any one of the vectors and is represented by closing side of the triangle taken in opposite order.

but in the question, we can see that the closing side of the triangle is in the opposite direction and equal in magnitude to that of the resultant of the remaining two vectors. hence the effect of the resultant of the two remaining vectors is cancelled by the closing side of the equilateral triangle. so the net resultant of this system of vectors is zero.

Inshallah - It will help you!