No, the vectors \( \mathbf{v_1} = (3, 4) \) and \( \mathbf{v_2} = (-3, 4) \) are not parallel.

To check if two vectors are parallel, one must be a scalar multiple of the other. In other words, there should exist a constant \( k \) such that \( \mathbf{v_2} = k \mathbf{v_1} \).

For \( \mathbf{v_1} = (3, 4) \) and \( \mathbf{v_2} = (-3, 4) \), if we assume \( \mathbf{v_2} = k \mathbf{v_1} \), this gives:

- \( -3 = 3k \) (from the first component)
- \( 4 = 4k \) (from the second component)

From the second equation, \( k = 1 \), but from the first equation, \( k = -1 \). Since these values of \( k \) are not consistent, the vectors are not scalar multiples of each other and hence are not parallel.

Would you like more details, or do you have any questions about this?

Here are 5 related questions:
1. How can you determine if two vectors are perpendicular?
2. What is the geometric interpretation of a scalar multiple of a vector?
3. What is the dot product, and how does it relate to parallelism?
4. How would you find the angle between two vectors?
5. Can two vectors of different magnitudes be parallel?

**Tip:** Two vectors are parallel if the angle between them is either 0° or 180°.

Explore whether the vectors (3, 4) and (-3, 4) are parallel. This problem involves vector algebra concepts such as scalar multiples and the conditions for parallelism. Detailed explanation and step-by-step solution provided. Suitable for high school students in Grades 10-12.

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