IF `vec(a),vec(b) and vec(c )` represent the three sides of a triangle as shown then using the properties of scalar product and vector product prove that
` . ` B/sinB = C/sinC

Explanation

To prove that \(\frac{B}{\sin B} = \frac{C}{\sin C}\) for the sides of a triangle represented by vectors \(\vec{A}\), \(\vec{B}\), and \(\vec{C}\), we can use the properties of scalar and vector products. Here’s a step-by-step solution:

### Step 1: Understand the Triangle and Vectors
Let \(\vec{A}\), \(\vec{B}\), and \(\vec{C}\) represent the sides of a triangle opposite to angles \(A\), \(B\), and \(C\) respectively. By the triangle law of vector addition, we can express one vector in terms of the others.

### Step 2: Express \(\vec{B}\) in Terms of \(\vec{A}\) and \(\vec{C}\)
From the triangle, we can write:
\[
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