“angle(between lines in space)”的概念、定义、翻译、参考文献-科学参考

angle(between lines in space)

Mathematics

Given two lines in space, let u₁ and u₂ be vectors with directions along the lines. Then the angle between the lines, even if they do not meet, is equal to the angle between the vectors u₁ and u₂ (see angle (between vectors)), with the directions of u₁ and u₂ chosen so that the angle θ‎ satisfies 0 ≤ θ‎ ≤ π‎/2 (θ‎ in radians), or 0 ≤ θ‎ ≤ 90 (θ‎ in degrees). If l₁, m₁, n₁ and l₂, m₂, n₂ are direction ratios for directions along the lines, the angle θ‎ between the lines is given by

$cos θ = \frac{| l_{1} 1_{2} + m_{1} m_{2} + n_{1} n_{2} |}{\sqrt{l_{1}^{2} + m_{1}^{2} + n_{1}^{2}} \sqrt{l_{2}^{2} + m_{2}^{2} + n_{2}^{2}}} .$

单词	angle(between lines in space)
释义	angle(between lines in space) Mathematics Given two lines in space, let u₁ and u₂ be vectors with directions along the lines. Then the angle between the lines, even if they do not meet, is equal to the angle between the vectors u₁ and u₂ (see angle (between vectors)), with the directions of u₁ and u₂ chosen so that the angle θ‎ satisfies 0 ≤ θ‎ ≤ π‎/2 (θ‎ in radians), or 0 ≤ θ‎ ≤ 90 (θ‎ in degrees). If l₁, m₁, n₁ and l₂, m₂, n₂ are direction ratios for directions along the lines, the angle θ‎ between the lines is given by $cos θ = \frac{\| l_{1} 1_{2} + m_{1} m_{2} + n_{1} n_{2} \|}{\sqrt{l_{1}^{2} + m_{1}^{2} + n_{1}^{2}} \sqrt{l_{2}^{2} + m_{2}^{2} + n_{2}^{2}}} .$
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