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**Hint:**The given charges are kept at the vertices A, B and c respectively of an equilateral triangle ABC of \[10cm\]. Also we have to find the resultant force on the charge at the vertex C.

Consider a closed ABC triangle, and C will take a force on the charge. The diagram shown below.

**Complete step by step answer:**

The diagram will be like this,

An equiangular triangle has three equal sides and angles. It will always have an angle of ${60^ \circ }$ in each corner.

Component of force due to B and A in x direction acting on C cancel out each other

\[\therefore {F_x} = 0\]

In $y$ direction forces add up

We get ${F_x} = \dfrac{{k(1\mu C)(2\mu C)}}{{{{(10 \times {{10}^{ - 2}})}^2}}} \times \sin 60 \times 2$

Substitute the values, and $\sin 60 = \dfrac{{\sqrt 3 }}{2}$

$ \Rightarrow \dfrac{{9 \times {{10}^9} \times 1 \times {{10}^{ - 6}} \times 2 \times {{10}^{ - 6}}}}{{100 \times {{10}^{ - 6}}}} \times \dfrac{{\sqrt 3 }}{2} \times 2$

Cancelling the same term and multiply to the remaining terms, we get

So we get,

$ \Rightarrow 3.1176N$

**So, The correct answer is option (D).**

**Additional information:**

In geometry, a triangle may be a closed, two-dimensional shape with three straight sides. A triangle is also a polygon. A triangle with all sides equilateral, a triangle with two sides equal is called isosceles, and a triangle with all sides a different length is called scalene.

**Note:**Triangles are often broadly classified into two types, which are:

Triangle based on the lengths of their sides

A) According to the lengths of their sides, triangles can be classified into three types with are:

i) Scalene

ii) Isosceles

iii) Equilateral

Triangles based on the their interior angles

B) According to the their interior angles, triangles can be classified into three types with are:

i) Acute-angled

ii) Obtuse-angled

iii) Right-angled

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