1 The right-handed screw rule

To understand how the vector product is formed it is helpful to consider first the right-handed screw rule. Consider the two vectors $\underset{̲}{a}$ and $\underset{̲}{b}$ shown in Figure 37.

Figure 37

The two vectors lie in a plane; this plane is shaded in Figure 37. Figure 38 shows the same two vectors and the plane in which they lie together with a unit vector, denoted $\stackrel{̂}{\underset{̲}{e}}$ , which is perpendicular to this plane. Imagine turning a right-handed screw, aligned along $\underset{̲}{ê}$ , in the direction from $\underset{̲}{a}$ towards $\underset{̲}{b}$ as shown. A right-handed screw is one which when turned clockwise enters the material into which it is being screwed (most screws are of this kind). You will see from Figure 38 that the screw will advance in the direction of $\stackrel{̂}{\underset{̲}{e}}$ .

Figure 38

On the other hand, if the right-handed screw is turned from $\underset{̲}{b}$ towards $\underset{̲}{a}$ the screw will retract in the direction of $\underset{̲}{\stackrel{̂}{f}}$ as shown in Figure 39.

Figure 39

We are now in a position to describe the vector product.