Consider the two vectors a and b shown in Figure 29.b
θa
Figure 29: Two vectors subtend an angle θ
Note that the tails of the two vectors coincide and that the angle between the vectors is labelled θ. Their scalar product, denoted by a · b, is defined as the product |a| |b| cos θ. It is very important to use the dot in the formula. The dot is the specific symbol for the scalar product, and is the reason why the scalar product is also known as the dot product. You should not use a × sign in this context because this sign is reserved for the vector product which is quite different.
The angle θ is always chosen to lie between 0 and π, and the tails of the two vectors must coincide. Figure 30 shows two incorrect ways of measuring θ.
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