数据结构与算法_求两个向量的夹角

Dear 丶 2023-06-18 03:59 5阅读 0赞

已知两个非零向量，作![在这里插入图片描述][20191130081356991.png]在空间任取一点O，作![在这里插入图片描述][20191130081519630.png]，则![在这里插入图片描述][20191130081547315.png]称为向量![20191130081614344.png][]的夹角，如下图当![seta等于零][seta]，两向量同向，否则等于180度两向量反向。![在这里插入图片描述][201911300818471.png]  
求两向量的公式为：  
![两向量夹角公式][20191130081933402.png]  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MzkxNjc1NQ_size_16_color_FFFFFF_t_70]

## C++代码如下： ##

#include<iostream>
    #include<cmath>
    using namespace std;
    #define PI 3.141592653
    int main()
    { 
    	float a[4];// 存放第一个向量的起点和重点
    	float b[4];// 存放第二个向量的起点和重点
    	cout << "请输入第一个向量的起点坐标:" << endl;
    	cin >> a[0] >> a[1];
    	cout << "请输入第一个向量的终点坐标:" << endl;
    	cin >> a[2] >> a[3];
    	cout << "请输入第二个向量的起点坐标:" << endl;
    	cin >> b[0] >> b[1];
    	cout << "请输入第二个向量的终点坐标:" << endl;
    	cin >> b[2] >> b[3];
    	float vector1x = a[0] - a[2];
    	float vector1y = a[1] - a[3];
    	float vector2x = b[0] - b[2];
    	float vector2y = b[1] - b[3];
    	float t = ((vector1x)*(vector2x) + (vector1y)*(vector2y))/ (sqrt(pow(vector1x, 2) + pow(vector1y, 2))*sqrt(pow(vector2x, 2) + pow(vector2y, 2)));
    	cout << "这两个向量的夹角为:" << acos(t)*(180 / PI) << "度" << endl;
    	system("pause");
    	return 0;
    }

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MzkxNjc1NQ_size_16_color_FFFFFF_t_70 1]

[20191130081356991.png]: https://img-blog.csdnimg.cn/20191130081356991.png
[20191130081519630.png]: https://img-blog.csdnimg.cn/20191130081519630.png
[20191130081547315.png]: https://img-blog.csdnimg.cn/20191130081547315.png
[20191130081614344.png]: https://img-blog.csdnimg.cn/20191130081614344.png
[seta]: https://img-blog.csdnimg.cn/20191130081705607.png
[201911300818471.png]: https://img-blog.csdnimg.cn/201911300818471.png
[20191130081933402.png]: https://img-blog.csdnimg.cn/20191130081933402.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MzkxNjc1NQ_size_16_color_FFFFFF_t_70]: https://img-blog.csdnimg.cn/20191130112656678.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MzkxNjc1NQ==,size_16,color_FFFFFF,t_70
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MzkxNjc1NQ_size_16_color_FFFFFF_t_70 1]: https://img-blog.csdnimg.cn/20191130112755895.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80MzkxNjc1NQ==,size_16,color_FFFFFF,t_70