STATEMENT-1 : Let `P(veca),Q(vecb)` and `R(vecc)` be three points such that `2veca+3vecb+5vecc=0`. Then the vector area of the `DeltaPQR` is a null vector.
And
STATEMENT-2 : Three collinear points from a triangle with zero area.

Options

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

Answer

To solve the problem, we need to analyze the statements provided and verify their correctness step by step.

### Given:
- **Statement 1**: \(2\vec{a} + 3\vec{b} + 5\vec{c} = 0\). This implies a relationship between the vectors \(\vec{a}\), \(\vec{b}\), and \(\vec{c}\).
- **Statement 2**: Three collinear points form a triangle with zero area.

### Step-by-Step Solution:

1. **Understanding the Equation**:
\[ 2\vec{a} + 3\vec{b} + 5\vec{c} = 0 \]
This equation can be rearranged to express one vector in terms of the others:
\[ 5\vec{c} = -2\vec{a} - 3\vec{b} \]
This indicates that \(\vec{c}\) can be expressed as a linear combination of \(\vec{a}\) and \(\vec{b}\). Therefore, the vectors \(\vec{a}\), \(\vec{b}\), and \(\vec{c}\) are collinear.

**Hint**: Check if the vectors can be expressed as multiples of each other to confirm collinearity.

2. **Vector Area of Triangle**:
The area of triangle \(PQR\) formed by points \(P(\vec{a})\), \(Q(\vec{b})\), and \(R(\vec{c})\) can be calculated using the formula for the area of a triangle formed by vectors:
\[ \text{Area} = \frac{1}{2} |\vec{PQ} \times \vec{PR}| \]
Where \(\vec{PQ} = \vec{b} - \vec{a}\) and \(\vec{PR} = \vec{c} - \vec{a}\).

3. **Collinearity Implication**:
Since \(\vec{a}\), \(\vec{b}\), and \(\vec{c}\) are collinear, the vectors \(\vec{PQ}\) and \(\vec{PR}\) will also be collinear. The cross product of two collinear vectors is zero:
\[ \vec{PQ} \times \vec{PR} = 0 \]
Therefore, the area of triangle \(PQR\) is:
\[ \text{Area} = \frac{1}{2} \cdot 0 = 0 \]

**Hint**: Remember that the area of a triangle is zero if the points are collinear.

4. **Conclusion**:
- **Statement 1** is true because the area of triangle \(PQR\) is indeed a null vector (zero area).
- **Statement 2** is also true as it correctly states that three collinear points form a triangle with zero area.
- Thus, Statement 2 provides a correct explanation for Statement 1.

### Final Answer:
Both statements are correct, and Statement 2 is the correct explanation for Statement 1.

**Correct Option**: A (Both statements are true, and Statement 2 explains Statement 1).