Question

a set of vectors taken in a given order gives a closed polygon then the resultant of these vectors is a

Answer 1

A set of vectors taken in a given order gives a closed polygon then the resultant of these vectors is a null vector.

Answer 2

Answer:

Null vector

Explanation:

Lets take an example of a hexagon, and according to your question, vectors a1, a2, a3, a4, a5, a6 make the side of the hexagon in the order as shown in the figure.

Now, from triangle law of vector addition,

a1 + a2 = b1

a1 + a2 = b1b1 + a3 = b2

a1 + a2 = b1b1 + a3 = b2b2 + a4 = b3

a1 + a2 = b1b1 + a3 = b2b2 + a4 = b3b3 + a5 = b4

Also, b4 = -a6

So, b4 + a6 = 0

So, the vectors added in an order gave a null vector.

Similarly,If a set of vectors taken in a given order gives a closed polygon, then the resultant of these vectors, will be a null vector.