Problem:
Three vectors each of magnitude A are acting at a point such that the angle between any two consecutive vectors in the same plane is 60 degrees. Find the magnitude of their resultant.

Solution:
To solve this problem, we will use the method of vector addition. Let us denote the three vectors by A, B, and C. We can represent these vectors graphically as shown in the figure below.



Step 1: Resolve the vectors into their components

We can resolve each vector into its components along the x and y-axes. Let us assume that the vectors are in the positive x-direction. Then, the components of the vectors are given by:

A = (Acos(0), Asin(0)) = (A, 0)
B = (Acos(60), Asin(60)) = (A/2, A*(√3)/2)
C = (Acos(120), Asin(120)) = (-A/2, A*(√3)/2)

Step 2: Add the components along the x and y-axes

To find the resultant of the three vectors, we need to add the components of the vectors along the x and y-axes separately. The x-component of the resultant is given by:

Rx = Ax + Bx + Cx
= A + A/2 - A/2
= (3/2)A

The y-component of the resultant is given by:

Ry = Ay + By + Cy
= 0 + A*(√3)/2 + A*(√3)/2
= A*(√3)

Step 3: Find the magnitude of the resultant

The magnitude of the resultant is given by:

R = √(Rx^2 + Ry^2)
= √[(3/2)A^2 + (A*(√3))^2]
= √(9/4)A^2 + 3A^2
= √(21/4)A^2
= (√21/2)A

Therefore, the magnitude of the resultant is (√21/2)A.

Conclusion:
In summary, we can find the magnitude of the resultant of three vectors by resolving the vectors into their components, adding the components along the x and y-axes separately, and then finding the magnitude of the resultant using the Pythagorean theorem. In this problem, the magnitude of the resultant is (√21/2)A.

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