#### Question

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

#### Solution 1

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.

#### Solution 2

(a) We cannot associate a vector with the length of a wire bent into a loop. This is because the length of the loop does not have a definite direction.

(b) We can associate a vector with a plane area. Such a vector is called area vector and its direction is represented by a normal drawn outward to the area.

(c) The area of a sphere does not point in any difinite direction. However, we can associate a null vector with the area of the sphere. We cannot associate a vector with the volume of a sphere.