` vec a , vec b ,a n d vec c` are three unit vectors and every two are inclined to each other at an angel `cos^(-1)(3//5)dot` If ` vec axx vec b=p vec a+q vec b+r vec c ,w h e r ep ,q ,r` are scalars, then find the value of `qdot`

Explanation

To solve the problem step by step, we will use the properties of vectors, specifically the cross product and the dot product, along with the given conditions.

### Step-by-Step Solution:

1. **Understanding the Given Information**:
We have three unit vectors \( \vec{a}, \vec{b}, \vec{c} \) that are inclined to each other at an angle \( \cos^{-1}\left(\frac{3}{5}\right) \). This means that the dot products between any two of these vectors can be expressed as:
\[
\vec{a} \cdot \vec{b} = \frac{3}{5}, \quad \vec{b} \cdot \vec{c} = \frac{3}{5}, \quad \vec{c} \cdot \vec{a} = \frac{3}{5}
...