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Can you associate vectors with (a) the l...

Can you associate vectors with (a) the length of a wire bent into a loop, (b) a plane area, (c) a sphere? Explain.

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To determine whether vectors can be associated with the length of a wire bent into a loop, a plane area, and a sphere, we can analyze each case step by step. ### Step 1: Length of a Wire Bent into a Loop - **Analysis**: When a wire is bent into a loop, it forms a closed shape. At every point along the wire, the direction of the tangent vector changes. This means that there is no single direction that can be consistently associated with the entire loop. - **Conclusion**: Therefore, we cannot associate a vector with the length of a wire bent into a loop. ### Step 2: Plane Area - **Analysis**: A plane area can be represented by a vector known as the area vector. The direction of this vector is perpendicular (normal) to the surface of the plane. The magnitude of the vector corresponds to the area of the plane. ...
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