Laws of vector algebra and unit vectors

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1 Laws of vector algebra
2 Unit vectors

Laws of vector algebra

If $\bold{A}$ , $\bold{B}$ and $\bold{C}$ are vectors, and $m$ and $n$ are scalars, then
$\begin{array}{lll}1. & \bold{A} + \bold{B} = \bold{B} + \bold{A} & Communicative Law for Addition\\ 2. & \bold{A} + (\bold{B} + \bold{C}) = (\bold{A} + \bold{B}) + \bold{C} & Associative Law for Addition\\ 3. & m(n\bold{A}) = (mn)\bold{A} = n(m\bold{A}) & Associative Law for Multiplication\\ 4. & (m + n)\bold{A} = m\bold{A} + n\bold{A} & Distributive Law\\ 5. & m(\bold{A} + \bold{B}) = m\bold{A} + m\bold{B} & Distributive Law \end{array}$
Note that in these laws only multiplication of a vector by one or more scalars is defined.

Unit vectors

Unit vectors are vectors having unit length. If $\bold{A}$ is any vector with length $A > 0$ , then $\bold{A}/A$ is a unit vector, denoted by $\bold{a}$ , having the same direction as $\bold{A}$ .