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The problem asks: "In which case is the cross product of two vectors equal to zero?"

Let’s break this down:

1. **Cross product basics**: 
   The cross product of two vectors **A** and **B** is defined as a vector that is perpendicular to both **A** and **B** and has a magnitude equal to \(\|A\|\|B\|\sin(\theta)\), where \(\theta\) is the angle between **A** and **B**.

2. **Conditions for zero cross product**:
   - The magnitude of the cross product is proportional to \(\sin(\theta)\). 
   - \(\sin(0^\circ) = 0\) and \(\sin(180^\circ) = 0\), meaning the cross product is zero if the vectors are **parallel** (which corresponds to options B and D).
   - The cross product is also zero if one of the vectors is the **zero vector** (which is option C, and also corresponds to D).

3. **When it’s NOT zero**:
   - If the vectors are **perpendicular**, the cross product is **not** zero, as \(\sin(90^\circ) = 1\), so the magnitude is \(\|A\|\|B\|\).

**Correct answer**: The cross product is zero in cases where the vectors are **parallel** or one of them is a **zero vector**, which corresponds to **D: Both B and C**.

Would you like more details on any of these points? Here are some related questions:

1. What is the geometric meaning of the cross product?
2. How do we calculate the direction of the cross product?
3. Can you explain when two vectors are considered parallel?
4. Why does the zero vector affect the cross product?
5. How does the cross product differ from the dot product?

**Tip**: The cross product yields a vector that is orthogonal (perpendicular) to the plane formed by the original two vectors.

In which case is the cross product of two vectors equal to zero?

Explore the conditions under which the cross product of two vectors is equal to zero. Understand how parallel vectors and the zero vector affect the result. Suitable for students in Grades 10-12 studying vector algebra and cross product properties.

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