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The problem refers to the condition when the vector cross product of two vectors \( \vec{a} \times \vec{b} \) equals zero. This occurs when the two vectors are parallel or collinear. Mathematically, this happens when the sine of the angle between them is zero, meaning the angle is either \( 0^\circ \) or \( 180^\circ \), i.e., \( \vec{a} \parallel \vec{b} \).

Looking at the answer choices provided:

a. Vectors \( \vec{a} \) and \( \vec{b} \) form an angle of \( \pi/6 \) between them.  
b. Vectors \( \vec{a} \) and \( \vec{b} \) are collinear.  
c. Vectors \( \vec{a} \) and \( \vec{b} \) form an angle of \( \pi/4 \) between them.  
d. Vectors \( \vec{a} \) and \( \vec{b} \) are perpendicular.

The correct answer is:

**b. Vectors \( \vec{a} \parallel \vec{b} \), i.e., they are collinear.**

Would you like more details on how the vector cross product works?

Here are 5 related questions you might find useful:
1. What is the geometric interpretation of the cross product of two vectors?
2. How do you compute the magnitude of the cross product between two vectors?
3. In what cases would the cross product of two non-zero vectors be zero?
4. How can the cross product be used to determine the area of a parallelogram?
5. What is the relationship between the dot product and the angle between two vectors?

**Tip**: When two vectors are perpendicular, their cross product results in a maximum value, as \( \sin(90^\circ) = 1 \).

Векторний добуток a⃗⋅b⃗ векторів a⃗ і b⃗ дорівнює нулю, якщо вони колінеарні.

Learn how the vector cross product of two vectors equals zero when the vectors are parallel. This concept is essential for understanding vector algebra and its geometric interpretation. Suitable for high school students in Grades 10-12.

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