Statement 1: If the vectors `veca` and `vecc` are non collinear, then the lines `vecr=6veca-vecc+lamda(2vecc-veca)` and `vecr=veca-vecc+mu(veca+3vecc)` are coplanar.
Statement 2: There exists `lamda` and `mu` such that the two values of `vecr` in statement -1 become same

Options

A. Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1.
B. Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement-1.
C. Statement-1 is True, Statement-2 is False.
D. Statement-1 is False, Statement-2 is True.

Explanation

To solve the problem, we need to analyze the two lines given in vector form and determine if they are coplanar and if there exist values of \( \lambda \) and \( \mu \) such that the two lines intersect.

### Step-by-Step Solution:

1. **Write down the equations of the lines:**
The two lines are given as:
\[ \vec{r_1} = 6\vec{a} - \vec{c} + \lambda(2\vec{c} - \vec{a}) \]
\[ \vec{r_2} = \vec{a} - \vec{c} + \mu(\vec{a} + 3\vec{c}) \]

2. **Set the two equations equal to each other:**
For the lines to be coplanar, we can equate the two expressions for \( \vec{r} \):
\[ 6\vec{a} - \vec{c} + \lambda(2\vec{c} - \vec{a}) = \vec{a} - \vec{c} + \mu(\vec{a} + 3\vec{c}) \]

3. **Rearrange the equation:**
Move all terms to one side:
\[ (6 - \lambda - \mu)\vec{a} + (-1 + 2\lambda - 3\mu)\vec{c} = 0 \]

4. **Set up the system of equations:**
For the above vector equation to hold, the coefficients of \( \vec{a} \) and \( \vec{c} \) must both equal zero:
\[ 6 - \lambda - \mu = 0 \quad \text{(1)} \]
\[ -1 + 2\lambda - 3\mu = 0 \quad \text{(2)} \]

5. **Solve the first equation for \( \lambda \):**
From equation (1):
\[ \lambda = 6 - \mu \]

6. **Substitute \( \lambda \) into the second equation:**
Substitute \( \lambda \) into equation (2):
\[ -1 + 2(6 - \mu) - 3\mu = 0 \]
Simplifying this gives:
\[ -1 + 12 - 2\mu - 3\mu = 0 \]
\[ 11 - 5\mu = 0 \]
\[ 5\mu = 11 \implies \mu = \frac{11}{5} \]

7. **Find \( \lambda \):**
Substitute \( \mu \) back into the equation for \( \lambda \):
\[ \lambda = 6 - \frac{11}{5} = \frac{30}{5} - \frac{11}{5} = \frac{19}{5} \]

8. **Conclusion:**
We have found specific values for \( \lambda \) and \( \mu \):
\[ \lambda = \frac{19}{5}, \quad \mu = \frac{11}{5} \]
Since we have found values for \( \lambda \) and \( \mu \) that satisfy both equations, the two lines are coplanar, and thus, Statement 1 is true. Since we have shown that such \( \lambda \) and \( \mu \) exist, Statement 2 is also true.