## Concepts

### Vector

### Dot Product

$$
t(a \cdot b)=(ta)\cdot b, \ t \in \text{scalar}
$$

$$
a \cdot b = b \cdot a
$$

$$
(a+b) \cdot c = a \cdot c+b \cdot c
$$

$$
a \cdot a = |a|^2
$$

### Cross Product

$$
t(a \times b) = (ta)\times{b}, \ t \in \text{scalar}
$$

$$
a \times b = - b\times a
$$

$$
(a+b) \times c = a \times c+b \times c
$$

$$
a \times a = 0
$$

## 常见敌人

点到直线最短长度

点到面最短长度

直线到直线最短长度

直线到面最短长度

angle between two lines

angle between two planes