Multiplying Vector1

# Multiplying Vector1 - Multiplying Vectors Scalar Product...

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Multiplying Vectors - Scalar Product Two vectors and are shown in Figure 3.9. The angle between these two vectors is [phi]. The scalar product of and (represented by . ) is defined as: In a coordinate system in which the x, y and z-axes are mutual perpendicular, the following relations hold for the scalar product between the various unit vectors: Suppose that the vectors and are defined as follows: Figure 3.9. Scalar Product of vectors and . The scalar product of and can now be rewritten in terms of the scalar product between the unit vectors along the x, y and z-axes: Note that in deriving this equation, we have applied the following rule: An alternative derivation of the expression of the scalar product in terms of the components of the two vectors can be easily derived as follows (see Figure 3.10). The components of and are given by: Figure 3.10. Alternative Derivation of Scalar Product. a x = a cos(a) a y = a sin(a) b x = b cos([beta]) b y = b sin([beta]) The scalar product can now be obtained as follows:

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