Is the length of a circular loop in space is vector quantity?

Question

In my physics textbook, there was the following question:
Can you associate vectors with
(a) length of a wire bent into a loop,
(b) a plane area,
(c) a sphere? Explain.
I reasoned that length and area stay the same regardless, and was confused about the sphere. But I saw this answer regarding the area of a plane figure on Physics SE https://physics.stackexchange.com/a/14166/340651. Well, if that is true, if you can associate direction to a plane by describing the normal line through that plane, then you can also do that for a circular loop, by describing the line normal to the plane in which the loop is. But in the answer given in the back of the book, it was given that only a plane area can be associated with a vector. Why not the length of the loop? Is it because we are talking about the "length" only, which has only magnitude? This reasoning helped me to reason out why the plane area is a vector and not the loop length. Or is there some other reason? Is the loop always in a plane or does the question account for loops that lie in 3 dimensions and not in a single plane?