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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Solution

Answer: No; Yes; No

(a) One cannot associate a vector with the length of a wire bent into a loop.

(b) One can associate an area vector with a plane area. The direction of this vector is normal, inward or outward to the plane area.

(c) One cannot associate a vector with the volume of a sphere. However, an area vector can be associated with the area of a sphere.

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