向量加法
三角形法则
三角形法则就是<span class="equation-text" data-index="0" data-equation="\overrightarrow{AB}" contenteditable="false"><span></span><span></span></span>+<span class="equation-text" data-index="1" data-equation="\overrightarrow{BC}" contenteditable="false"><span></span><span></span></span>=<span class="equation-text" contenteditable="false" data-index="2" data-equation="\overrightarrow{AC}"><span></span><span></span></span>这种计算法则叫做向量加法的三角形法则，简记为：首尾相连、连接首尾、指向终点
平行四边形法则
交换律
<span class="equation-text" data-index="0" data-equation="\overrightarrow{a}+\overrightarrow{b}" contenteditable="false"><span></span><span></span></span>=<span class="equation-text" contenteditable="false" data-index="1" data-equation="\overrightarrow{b}+\overrightarrow{a}"><span></span><span></span></span>
结合律
<span class="equation-text" data-index="0" data-equation="(\overrightarrow{a}+\overrightarrow{b})" contenteditable="false"><span></span><span></span></span>+<span class="equation-text" data-index="1" data-equation="\overrightarrow{c}" contenteditable="false"><span></span><span></span></span>=<span class="equation-text" data-index="2" data-equation="\overrightarrow{a}" contenteditable="false"><span></span><span></span></span>+<span class="equation-text" contenteditable="false" data-index="3" data-equation="(\overrightarrow{b}+\overrightarrow{c})"><span></span><span></span></span>
<span class="equation-text" data-index="0" data-equation="\overrightarrow{a}" contenteditable="false"><span></span><span></span></span>与<span class="equation-text" contenteditable="false" data-index="1" data-equation="\overrightarrow{b}"><span></span><span></span></span>共线同向
<span class="equation-text" data-index="0" data-equation="\overrightarrow{OA}" contenteditable="false"><span></span><span></span></span>=<span class="equation-text" data-index="1" data-equation="\overrightarrow{a}" contenteditable="false"><span></span><span></span></span>,<span class="equation-text" data-index="2" data-equation="\overrightarrow{AB}" contenteditable="false"><span></span><span></span></span>=<span class="equation-text" data-index="3" data-equation="\overrightarrow{b}" contenteditable="false"><span></span><span></span></span>,则<span class="equation-text" data-index="4" data-equation="\overrightarrow{a}+\overrightarrow{b}" contenteditable="false"><span></span><span></span></span>=<span class="equation-text" contenteditable="false" data-index="5" data-equation="\overrightarrow{OB}"><span></span><span></span></span>
<span class="equation-text" data-index="0" data-equation="\overrightarrow{a}" contenteditable="false"><span></span><span></span></span>与<span class="equation-text" contenteditable="false" data-index="1" data-equation="\overrightarrow{b}"><span></span><span></span></span>共线反向
<span class="equation-text" data-index="0" data-equation="\overrightarrow{OA}" contenteditable="false"><span></span><span></span></span>=<span class="equation-text" data-index="1" data-equation="\overrightarrow{a}" contenteditable="false"><span></span><span></span></span>,<span class="equation-text" data-index="2" data-equation="\overrightarrow{AB}" contenteditable="false"><span></span><span></span></span>=<span class="equation-text" data-index="3" data-equation="\overrightarrow{b}" contenteditable="false"><span></span><span></span></span>,则<span class="equation-text" data-index="4" data-equation="\overrightarrow{a}+\overrightarrow{b}" contenteditable="false"><span></span><span></span></span>=<span class="equation-text" contenteditable="false" data-index="5" data-equation="\overrightarrow{OB}"><span></span><span></span></span>
等号成立，共线同向
|<span class="equation-text" data-index="0" data-equation="\overrightarrow{a}" contenteditable="false"><span></span><span></span></span>+<span class="equation-text" data-index="1" data-equation="\overrightarrow{b}" contenteditable="false"><span></span><span></span></span>|≤|<span class="equation-text" data-index="2" data-equation="\overrightarrow{a}" contenteditable="false"><span></span><span></span></span>|+|<span class="equation-text" contenteditable="false" data-index="3" data-equation="\overrightarrow{b}"><span></span><span></span></span>|
向量减法
<span class="equation-text" data-index="0" data-equation="\overrightarrow{a}" contenteditable="false"><span></span><span></span></span>和<span class="equation-text" contenteditable="false" data-index="1" data-equation="\overrightarrow{b}"><span></span><span></span></span>互为相反向量
<span class="equation-text" data-index="0" data-equation="\overrightarrow{a}" contenteditable="false"><span></span><span></span></span>=<span class="equation-text" data-index="1" data-equation="-\overrightarrow{b}" contenteditable="false"><span></span><span></span></span>,<span class="equation-text" data-index="2" data-equation="\overrightarrow{b}" contenteditable="false"><span></span><span></span></span>=-<span class="equation-text" data-index="3" data-equation="\overrightarrow{a}" contenteditable="false"><span></span><span></span></span>,<span class="equation-text" data-index="4" data-equation="\overrightarrow{a}+\overrightarrow{b}" contenteditable="false"><span></span><span></span></span>=<span class="equation-text" contenteditable="false" data-index="5" data-equation="\overrightarrow{0}"><span></span><span></span></span>
等号成立，共线反向
|<span class="equation-text" data-index="0" data-equation="\overrightarrow{a}" contenteditable="false"><span></span><span></span></span>+<span class="equation-text" data-index="1" data-equation="\overrightarrow{b}" contenteditable="false"><span></span><span></span></span>|≥|<span class="equation-text" data-index="2" data-equation="\overrightarrow{a}" contenteditable="false"><span></span><span></span></span>|-|<span class="equation-text" contenteditable="false" data-index="3" data-equation="\overrightarrow{b}"><span></span><span></span></span>|
向量数乘
一般地， 我们规定实数λ与向址a的积是一个向量，这种运算叫做向量的数乘，记作λa
当λ>0时，λa的方向与a的方向相同；当λ<0时，λa的方向与a的方向相反
(-1)a=-a
