STATEMENT-1 Let `veca,vecb` bo two vectors such that `veca.vecb=0`, then `veca` and `vecb` are perpendicular. And
STATEMENT-2 Two non-zero vectors are perpendicular if and only if their dot product is zero.

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

Answer

To solve the problem, we need to analyze both statements and determine their validity.

### Step 1: Understanding Statement 1
**Statement 1**: Let \(\vec{a}, \vec{b}\) be two vectors such that \(\vec{a} \cdot \vec{b} = 0\). Then \(\vec{a}\) and \(\vec{b}\) are perpendicular.

**Explanation**: The dot product of two vectors \(\vec{a}\) and \(\vec{b}\) is given by:
\[ \vec{a} \cdot \vec{b} = |\vec{a}| |\vec{b}| \cos \theta \]
where \(\theta\) is the angle between the two vectors. If \(\vec{a} \cdot \vec{b} = 0\), it implies:
\[ |\vec{a}| |\vec{b}| \cos \theta = 0 \]
Since \(|\vec{a}|\) and \(|\vec{b}|\) are non-zero (as they are vectors), we must have \(\cos \theta = 0\). This means:
\[ \theta = 90^\circ \]
Thus, \(\vec{a}\) and \(\vec{b}\) are indeed perpendicular.

### Step 2: Understanding Statement 2
**Statement 2**: Two non-zero vectors are perpendicular if and only if their dot product is zero.

**Explanation**: This statement is a direct consequence of the definition of the dot product. If two non-zero vectors \(\vec{a}\) and \(\vec{b}\) are perpendicular, then by definition, the angle \(\theta\) between them is \(90^\circ\). Therefore:
\[ \vec{a} \cdot \vec{b} = |\vec{a}| |\vec{b}| \cos 90^\circ = 0 \]
Conversely, if \(\vec{a} \cdot \vec{b} = 0\), we have already established that this implies \(\theta = 90^\circ\), meaning they are perpendicular. Hence, the statement is true.

### Conclusion
Both statements are true:
- **Statement 1** is true because \(\vec{a} \cdot \vec{b} = 0\) implies \(\vec{a}\) and \(\vec{b}\) are perpendicular.
- **Statement 2** is true because non-zero vectors are perpendicular if and only if their dot product is zero.

### Final Answer
The correct option is: **Both statements are true, and Statement 2 is a correct explanation for Statement 1.**

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