A vector `vec(a)` is turned without a change in its length through a small angle `d theta`. Find the value of `|Deltavec(a)|` and `Delta a`.

Explanation

To solve the problem, we need to analyze the change in the vector \( \vec{A} \) when it is turned through a small angle \( d\theta \) without changing its length.

### Step-by-Step Solution:

1. **Understanding the Initial and Final Vectors**:
- Let \( \vec{A} \) be the initial vector with a magnitude \( |\vec{A}| = A \).
- After turning the vector through a small angle \( d\theta \), the new vector can be denoted as \( \vec{A}' \).

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