Two lines `L_1: x=5, y/(3-alpha)=z/(-2)` and `L_2: x=alpha, y/(-1)=z/(2-alpha)` are coplanar. Then `alpha` can take value (s) a. `1` b. `2` c. `3` d. `4`

Options

A. 1
B. 2
C. 3
D. 4

Explanation

To determine the values of \( \alpha \) for which the lines \( L_1 \) and \( L_2 \) are coplanar, we will use the condition that the determinant formed by the direction ratios and the position vectors of the lines must be equal to zero.

### Step-by-Step Solution:

1. **Identify the lines**:
The lines are given as:
- \( L_1: x = 5, \frac{y}{3 - \alpha} = \frac{z}{-2} \)
- \( L_2: x = \alpha, \frac{y}{-1} = \frac{z}{2 - \alpha} \)
...