show that velocity and acceleration are contravariant vectors and that the gradient of a scalar field is a covariant vector.

Mr. M is walking to Mr. T’s house. He take the shortcut across an open field. His first displacement is 140 m[E35N]. He then walks 200.0m[E]. What is Mr. M’s total displacement?

Show that the directions of the isoline and the gradient line at any given points in a scalar field are orthogonal to each other.