## 2015年6月23日火曜日

### 数学 - 線型代数 - 2次元と3次元の簡単な幾何学 - ベクトルの加法と実数倍(成分表示)

• 数式入力ソフト(TeX, MathML): MathType
• MathML対応ブラウザ: Firefox、Safari
• MathML非対応ブラウザ(Internet Explorer, Google Chrome...)用JavaScript Library: MathJax

$\begin{array}{l}A=\left({a}_{1},{a}_{2}\right),B=\left({b}_{1},{b}_{2}\right),C=\left({c}_{1},{c}_{2}\right)\\ L=\left(\frac{{b}_{1}+{c}_{1}}{2},\frac{{b}_{2}+{c}_{2}}{2}\right)\\ M=\left(\frac{{c}_{1}+{a}_{1}}{2},\frac{{c}_{2}+{a}_{2}}{2}\right)\\ N=\left(\frac{{a}_{1}+{b}_{1}}{2},\frac{{a}_{2}+{b}_{2}}{2}\right)\end{array}$

1. $\begin{array}{l}\stackrel{\to }{BN}+\stackrel{\to }{CM}\\ =\left(\frac{{a}_{1}-{b}_{1}}{2},\frac{{a}_{2}-{b}_{2}}{2}\right)+\left(\frac{{a}_{1}-{c}_{1}}{2},\frac{{a}_{2}-{c}_{2}}{2}\right)\\ =\left({a}_{1}-\frac{{b}_{1}+{c}_{1}}{2},{a}_{2}-\frac{{b}_{2}+{c}_{2}}{2}\right)\\ =\stackrel{\to }{LA}\end{array}$

2. $\begin{array}{l}\stackrel{\to }{BL}+\stackrel{\to }{CM}+\stackrel{\to }{AN}\\ =\left(\frac{{c}_{1}-{b}_{1}}{2},\frac{{c}_{2}-{b}_{2}}{2}\right)+\left(\frac{{a}_{1}-{c}_{1}}{2},\frac{{a}_{2}-{c}_{2}}{2}\right)+\left(\frac{{b}_{1}-{a}_{1}}{2},\frac{{b}_{2}-{a}_{2}}{2}\right)\\ =\left(0,0\right)\\ =0\end{array}$