\n
Laws of vector algebra<\/h2>\n
If $\\bold{A}$ , $\\bold{B}$ and $\\bold{C}$ are vectors, and $m$ and $n$ are scalars, then<\/p>\n
$\\begin{array}{lll}1. & \\bold{A} + \\bold{B} = \\bold{B} + \\bold{A} & Communicative Law for Addition\\\\ 2. & \\bold{A} + (\\bold{B} + \\bold{C}) = (\\bold{A} + \\bold{B}) + \\bold{C} & Associative Law for Addition\\\\ 3. & m(n\\bold{A}) = (mn)\\bold{A} = n(m\\bold{A}) & Associative Law for Multiplication\\\\ 4. & (m + n)\\bold{A} = m\\bold{A} + n\\bold{A} & Distributive Law\\\\ 5. & m(\\bold{A} + \\bold{B}) = m\\bold{A} + m\\bold{B} & Distributive Law \\end{array}$ <\/p>\n
Note that in these laws only multiplication of a vector by one or more scalars is defined. <\/p>\n
Unit vectors<\/h2>\n
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 $\\bold{A}$ . <\/p>\n<\/blockquote>\n
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Laws of vector algebra<\/h2>\nIf , and are vectors, and and are scalars, then<\/p>\n<\/p>\nNote that in these laws only multiplication of a vector by one or more scalars is defined. <\/p>\n