A vector A is turned by a very small angle Δθ radians (where Δθ is much less than 1) to form a new vector B. What is the magnitude of the difference |B − A|?

|A| Δθ
|B| Δθ − |A|
|A| Δθ² / 2
0

Correct answer: |A| Δθ

Solution

For a small angle Δθ, the magnitude of the difference |B − A| is approximately |A| Δθ, as the arc length of the rotation is proportional to the angle and the magnitude of the vector.

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