Statement-I : The angle between vectors `vec(A)xxvec(B)` and `vec(B)xxvec(A)` is `pi` radian.
Statement-II : `vec(B)xxvec(A)=-vec(A)xx vec(B)`

A. Statement-I is true, Statement-II is true, Statement-II is correct explanation for statement-I
B. Statement-I is true, Statement-II is true, Statement-II is NOT a correct explanation for statement-I
C. Statement-I is true, Statement-II is false.
D. Statement-I is true, Statement-II is false.

Options

A. Statement-I is true, Statement-II is true, Statement-II is correct explanation for statement-I
B. Statement-I is true, Statement-II is true, Statement-II is NOT a correct explanation for statement-I
C. Statement-I is true, Statement-II is false.
D. Statement-I is false and Statement-II is true.

Answer

To solve the given question, we need to analyze both statements provided and determine their validity and relationship.

### Step 1: Analyze Statement-I
Statement-I claims that the angle between the vectors \(\vec{A} \times \vec{B}\) and \(\vec{B} \times \vec{A}\) is \(\pi\) radians (or 180 degrees).

- The cross product of two vectors \(\vec{A}\) and \(\vec{B}\) is defined as:
\[ \vec{A} \times \vec{B} = |\vec{A}| |\vec{B}| \sin(\theta) \hat{n} \]
where \(\theta\) is the angle between the vectors and \(\hat{n}\) is the unit vector perpendicular to the plane containing \(\vec{A}\) and \(\vec{B}\).

- The cross product is anti-commutative, meaning:
\[ \vec{B} \times \vec{A} = -(\vec{A} \times \vec{B}) \]

- Therefore, \(\vec{B} \times \vec{A}\) points in the opposite direction to \(\vec{A} \times \vec{B}\).

- Since they point in opposite directions, the angle between them is indeed \(\pi\) radians.

**Conclusion for Statement-I**: True.

### Step 2: Analyze Statement-II
Statement-II states that \(\vec{B} \times \vec{A} = -\vec{A} \times \vec{B}\).

- As mentioned earlier, this is a property of the cross product, confirming that reversing the order of the vectors results in a vector that is equal in magnitude but opposite in direction.

**Conclusion for Statement-II**: True.

### Step 3: Determine the Relationship Between the Statements
- Since both statements are true, we need to check if Statement-II provides a correct explanation for Statement-I.

- Statement-II explains that the vectors \(\vec{A} \times \vec{B}\) and \(\vec{B} \times \vec{A}\) are equal in magnitude but opposite in direction, which directly leads to the conclusion that the angle between them is \(\pi\) radians.

**Conclusion**: Statement-II is indeed a correct explanation for Statement-I.

### Final Answer
The correct option is:
**A. Statement-I is true, Statement-II is true, Statement-II is correct explanation for Statement-I.**

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