Differentiation of Vectors

Abstract

Consider a bug moving along some curve in 3-dimensional space. The position of the bug at timetis given by the three coordinates

$$\left( {x\left( t \right),y\left( t \right),z\left( t \right)} \right),$$

which depend on t. We abbreviate these by X(t). For instance, the position of a bug moving along a straight line was seen in the preceding chapter to be given by

$$X\left( t \right) = P + tA,$$

where Pis the starting point, and A gives the direction of the bug. However, we can give examples when the bug does not move on a straight line. First we look at an example in the plane.