7. Cartesian coordinates in three dimensions





If a vector is expressed in Cartesian form, then it’s easy to calculate any scalar multiple of that vector in Cartesian form. The general rule is that given any vector v = xi + yj + zk and any scalar a, then
For example, if v = 2i + j  k, then 4v = 8i  4j + 4k. The same formula applies in two dimensions. The vector v = xi + yj can be thought of as v = xi + yj + 0k. Then if a is any scalar,
Thus if u = 2i + j then 2u = 4i + 2j, as illustrated in the following picture.


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