Can you associate vectors with (a) the length of a wire bent into a loop, (b) a plane area, (c) a sphere ? Explain.
(a)
A vector can be associated only with those physical quantities that have a magnitude as well as a definite direction. The length of a wire bent into a loop does not have a definite direction.
Thus, we cannot associate a vector with the length of a wire bent into a loop.
(b)
A vector can be associated only with those physical quantities that have a magnitude as well as a definite direction. A plane area has magnitude as well as a definite direction. The area vector has direction normal, inward or outward to the plane.
Thus, we can associate a vector with a plane area.
(c)
A vector can be associated only with those physical quantities that have a magnitude as well as a definite direction. The volume of the sphere does not have a definite direction. However, an area vector can be associated with the area of the sphere.
Thus, we cannot associate a vector with the sphere.
(a)
A vector can be associated only with those physical quantities that have a magnitude as well as a definite direction. The length of a wire bent into a loop does not have a definite direction.
Thus, we cannot associate a vector with the length of a wire bent into a loop.
(b)
A vector can be associated only with those physical quantities that have a magnitude as well as a definite direction. A plane area has magnitude as well as a definite direction. The area vector has direction normal, inward or outward to the plane.
Thus, we can associate a vector with a plane area.
(c)
A vector can be associated only with those physical quantities that have a magnitude as well as a definite direction. The volume of the sphere does not have a definite direction. However, an area vector can be associated with the area of the sphere.
Thus, we cannot associate a vector with the sphere.
