The maximum number of points of intersections of three lines drawn in a plane is

Options

A. 1
B. 2
C. 3
D. 6

Answer

To find the maximum number of points of intersection of three lines drawn in a plane, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Intersection Points**:
- When two lines intersect, they can create a point of intersection. The maximum number of intersection points occurs when no two lines are parallel and no three lines are concurrent (i.e., they do not all meet at a single point).

2. **Calculating Points of Intersection**:
- For each pair of lines, there can be one point of intersection.
- The formula to calculate the number of intersection points from 'n' lines is given by the combination formula \( C(n, 2) \), which represents the number of ways to choose 2 lines from 'n' lines.

3. **Applying the Formula**:
- For three lines (n = 3), we calculate the number of intersection points:
\[ C(3, 2) = \frac{3!}{2!(3-2)!} = \frac{3 \times 2 \times 1}{2 \times 1 \times 1} = 3 \]

4. **Conclusion**:
- Therefore, the maximum number of points of intersection of three lines drawn in a plane is **3**.