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Vector Arithmetic

# Vector Arithmetic - Vector Arithmetic In this section we...

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Vector Arithmetic In this section we need to have a brief discussion of vector arithmetic. We’ll start with addition of two vectors. So, given the vectors and the addition of the two vectors is given by the following formula. The following figure gives the geometric interpretation of the addition of two vectors. This is sometimes called the parallelogram law or triangle law . Computationally, subtraction is very similar. Given the vectors and the difference of the two vectors is given by, Here is the geometric interpretation of the difference of two vectors.

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It is a little harder to see this geometric interpretation. To help see this let’s instead think of subtraction as the addition of and . First, as we’ll see in a bit is the same vector as with opposite signs on all the components. In other words, goes in the opposite direction as . Here is the vector set up for . As we can see from this figure we can move the vector representing to the position we’ve got in the first figure showing the difference of the two vectors. Note that we can’t add or subtract two vectors unless they have the same number of components. If they don’t have the same number of components then addition and subtraction can’t be done.
The next arithmetic operation that we want to look at is scalar multiplication . Given the vector and any number c the scalar multiplication is,

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Vector Arithmetic - Vector Arithmetic In this section we...

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