If the point `(a^2,a+1)` lies in the angle between the lines `3x-y+1=0` and `x+2y-5=0` containing the origin, then find the value of `adot`

Explanation

To solve the problem, we need to determine the value of \( a \) such that the point \( (a^2, a + 1) \) lies in the angle between the lines given by the equations \( 3x - y + 1 = 0 \) and \( x + 2y - 5 = 0 \), both containing the origin.

### Step 1: Identify the lines
The equations of the lines can be rewritten in slope-intercept form to find their slopes:
1. For the line \( L_1: 3x - y + 1 = 0 \):
\[ y = 3x + 1 \]
...