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Multiplying Vectors

Multiplying Vectors - Multiplying Vectors Multiplying a...

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Multiplying Vectors - Multiplying a Vector by a Scalar The product of a vector and a scalar s is a new vector, whose direction is the same as that of if s is positive or opposite to that direction if s is negative (see Figure 3.8). The magnitude of the new vector is the magnitude of multiplied by the absolute value of s. This procedure can be summarized as follows: Figure 3.8. Multiplying a vector by a scalar. Since two vectors are only equal only if their corresponding components are equal, we obtain the following relation between the components of and the components of : The following relations are summarizing the relations between the magnitude and direction of the vectors and : 3.3. 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:

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Figure 3.9. Scalar Product of vectors
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Multiplying Vectors - Multiplying Vectors Multiplying a...

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