If `P_1:vec r.vecn_1-d_1=0` `P_2:vec r.vec n_2-d_2=0` and `P_3:vec r.vecn_3-d_3=0` are three non-coplanar vectors, then three lines `P_1= 0`, `P_2=0`; `P_2=0`,`P_3=0` ; `P_3=0` `P_1=0` are

Options

A. parallel lines
B. coplanar lines
C. coincident lines
D. concurrent lines

Explanation

To solve the problem, we need to analyze the given planes and their corresponding lines. The planes are defined by the equations:

1. \( P_1: \vec{r} \cdot \vec{n_1} - d_1 = 0 \)
2. \( P_2: \vec{r} \cdot \vec{n_2} - d_2 = 0 \)
3. \( P_3: \vec{r} \cdot \vec{n_3} - d_3 = 0 \)

These equations represent three planes in three-dimensional space defined by their normal vectors \( \vec{n_1}, \vec{n_2}, \vec{n_3} \) and constants \( d_1, d_2, d_3 \).

### Step 1: Identify the Lines
The lines defined by the equations \( P_1 = 0 \), \( P_2 = 0 \), and \( P_3 = 0 \) represent the intersections of the planes:

- The line \( P_1 = 0 \) is the intersection of the planes \( P_1 \) and \( P_2 \).
- The line \( P_2 = 0 \) is the intersection of the planes \( P_2 \) and \( P_3 \).
- The line \( P_3 = 0 \) is the intersection of the planes \( P_3 \) and \( P_1 \).

### Step 2: Analyze Non-Coplanarity
Since the planes are defined by non-coplanar vectors, it implies that the normal vectors \( \vec{n_1}, \vec{n_2}, \vec{n_3} \) are not all lying in the same plane. This means that the three planes intersect at a unique point, which is a characteristic of non-coplanar planes.

### Step 3: Determine the Nature of the Lines
Given that the planes are non-coplanar, the lines formed by their intersections will also be concurrent. This means that all three lines intersect at a single point in space.

### Conclusion
Thus, the lines defined by the equations \( P_1 = 0 \), \( P_2 = 0 \), and \( P_3 = 0 \) are concurrent lines. Therefore, the correct answer is:

**Option D: Concurrent**