# OEF 3维向量 --- 介绍 ---

### 平行四边形面积

(,,) , (,,) , (,,) , (,,) .

### 三角形面积

(,,) , (,,) , (,,) .

, , .

### 组合

v1 = (,,) , v2 = (,,) , v3 = (,,)

v = .

### 2个向量的组合

v1 = (,,) , v2 = (,,)

v = .

### 4个向量的组合

v1 = (,,) , v2 = (,,) , v3 = (,,) , v4 = (,,)

v = .

### 求向量的组合

v1 = (,,) , v2 = (,,) , v3 = (,,)

v = av1 + bv2 + cv3 .

### 求两个向量的组合

v1 = (,,) , v2 = (,,)

v = av1 + bv2 .

### 已知内积

v1 = (,,) , v2 = (,,) , v3 = (,,)

<v,v1> = , <v,v2> = , <v,v3> = .

u v = (,,) .

### 平行四边形的顶点

A = (,,) , B = (,,) , C = (,,) .

### 与两个向量垂直

v1 = (,,) , v2 = (,,)

### 线性关系

v1 = (,,) , v2 = (,,) , v3 = (,,) , v4 = (,,) .

a v1 + b v2 + c v3 + d v4 = 0 ,

### 平行六面体体积

B = (,,) , C = (,,) , D = (,,) .

### 四面体体积

A = (,,) , B = (,,) , C = (,,) , D = (,,) .

Description: 关于3维向量的一组练习. interactive exercises, online calculators and plotters, mathematical recreation and games

Keywords: interactive mathematics, interactive math, server side interactivity, algebra, linear algebra, geometry, vector, cross product, addition, linear combination, polygon, polyhedron, parallelogramme, parallelepipede