내적과 외적(Dot Product & Cross Product)

[20.01.08 updated]

벡터 $A$와 $B$에 관하여,

내적 (Dot Product, Inner Product, Scalar Product)

\[{A}\cdot{B} = \sum_{k=1}^n(A_k B_k) =|A||B|cos\theta\]

외적 (Cross Product, Outer Product, Vector Product)

\[A\times B= det\begin{vmatrix} a & b & c \\ d & e & f \\ g & h & i \end{vmatrix} \\ = a\cdot det\begin{vmatrix}e & f\\h&i \end{vmatrix} - b\cdot det\begin{vmatrix}d & f\\g&i \end{vmatrix} + c\cdot det\begin{vmatrix}d & e\\g&h \end{vmatrix} \\ = a(ei-fh) - b(di-fg) + c(dh-eg)\] \[|A\times B| = |A||B|sin\theta\]