Associative law is obeyed by

Options

A. Addition of vectors
B. subtraction of vectors
C. both
D. none

Answer

**Step-by-Step Solution:**

1. **Understanding Associative Law**: The associative law states that when adding or multiplying three or more numbers (or vectors), the way in which the numbers are grouped does not change the result. In mathematical terms, for any three elements \( a, b, c \):
- For addition: \( (a + b) + c = a + (b + c) \)
- For multiplication: \( (a \times b) \times c = a \times (b \times c) \)

2. **Applying Associative Law to Vectors**: In the context of vectors, the associative law can be applied to vector addition. If we have three vectors \( \vec{A}, \vec{B}, \vec{C} \):
- According to the associative law for vectors:
\[ (\vec{A} + \vec{B}) + \vec{C} = \vec{A} + (\vec{B} + \vec{C}) \]
- This means that regardless of how we group the vectors when adding them, the resultant vector will be the same.

3. **Subtraction of Vectors**: However, the associative law does not hold for vector subtraction. For example, if we consider:
- \( (\vec{A} - \vec{B}) - \vec{C} \) and \( \vec{A} - (\vec{B} - \vec{C}) \)
- These two expressions will not yield the same result, demonstrating that subtraction does not obey the associative law.

4. **Conclusion**: Therefore, the associative law is obeyed by vector addition but not by vector subtraction.

**Final Answer**: The associative law is obeyed by vector addition.

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