🧭 单位向量计算器Unit Vector Calculator
输入 2–10 维向量，求它的模长和同方向的单位向量 û = v ÷ |v|；整数分量时给出带根号的精确形式，二维和三维还给出方向角。Enter a vector with 2 to 10 components to get its magnitude and the unit vector in the same direction, û = v ÷ |v| — exact with square roots for whole-number components, plus direction angles in 2D and 3D.
使用说明与常见问题How-to & FAQ
「单位向量计算器」是什么？What is the Unit Vector Calculator tool?
输入 2–10 维向量，求它的模长和同方向的单位向量 û = v ÷ |v|；整数分量时给出带根号的精确形式，二维和三维还给出方向角。Enter a vector with 2 to 10 components to get its magnitude and the unit vector in the same direction, û = v ÷ |v| — exact with square roots for whole-number components, plus direction angles in 2D and 3D.
如何使用「单位向量计算器」？How do I use the Unit Vector Calculator tool?
在「单位向量计算器」中，填写「向量（如 3, 4 或 1 2 2）」等参数，结果会随输入实时计算并显示在下方。In the Unit Vector Calculator: Fill in "Vector (e.g. 3, 4 or 1 2 2)"; results are recalculated instantly as you type.
单位向量怎么求？How is a unit vector found?
用向量除以它的模长：û = v ÷ |v|，其中 |v| = √(v₁² + v₂² + …)。单位向量模长为 1，方向与原向量相同。Divide the vector by its magnitude: û = v ÷ |v|, where |v| = √(v₁² + v₂² + …). The result has length 1 and points the same way.
精确形式是怎么来的？Where does the exact form come from?
分量都是整数时，把 |v| 化成 k√r，再把每个分量除以它并有理化分母，例如 (2, 4) 的模长为 2√5，单位向量为 (√5/5, 2√5/5)。With whole-number components, |v| is simplified to k√r and each component is divided by it with the denominator rationalized: (2, 4) has magnitude 2√5 and unit vector (√5/5, 2√5/5).
计算精度如何？How precise are the results?
「单位向量计算器」使用 JavaScript 双精度浮点数（约 15–16 位有效数字）；极大或极小的数值可能存在精度误差。The Unit Vector Calculator uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.
「单位向量计算器」免费吗？需要注册吗？Is the Unit Vector Calculator free? Do I need an account?
「单位向量计算器」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Unit Vector Calculator is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.