change 三维思考

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1AoB 2023-11-06 00:18:48 +08:00
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@ -43,8 +43,49 @@ This article offers a sample of basic Markdown.
![1699198980225](图片/1699198980225.png) ![1699198980225](图片/1699198980225.png)
### 叉乘:
![1699200464682](图片/1699200464682.png)
ax1y1bx2y2则a×b=x1\*y2-x2\*y1
---
![1699200969023](图片/1699200969023.png)
```
顶点一:(0,0,0)
顶点二:(1,0,0)
顶点三:(0,1,0)
向量a = (1,0,0)-(0,0,0) = (1,0,0) = (a₁,a₂,a₃)
向量b = (0,1,0)-(0,0,0) = (0,1,0) = (b₁,b₂,b₃)
axb = (0,0,1)
```
至于为啥 (1,0,0) $X$ (0,1,0) = (0,0,1)?
根据叉积的计算公式为:==23 32, 31 13,12 21==
$a × b$ = ($a₂b₃$- $a₃b₂$, $a₃b₁$ - $a₁b₃$, $a₁b₂$ - $a₂b₁$)
=(0\*0-0\*1, 0\*0-1\*0, 1\*1-0\*0)
=(0, 0 ,1)
![1699200939039](图片/1699200939039.png)
### 点乘:(完整)
![1699199213786](图片/1699199213786.png)
上面是二维,下面是三维:
V1( x1, y1, z1)·V2(x2, y2, z2) = x1\*x2 + y1\*y2 + z1\*z2
## 继续这道题
![1699199213786](图片/1699199213786.png) ## 四元数又是什么?
![1699200693103](图片/1699200693103.png)

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