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lecture_24
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| Both sides previous revisionPrevious revisionNext revision | Previous revision | ||
| lecture_24 [2015/04/23 12:03] – rupert | lecture_24 [2016/01/22 19:06] (current) – rupert | ||
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| + | ~~REVEAL~~ | ||
| ===== The distance from a point to a line ===== | ===== The distance from a point to a line ===== | ||
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| Let $\vv_1$ be a direction vector along $L_1$, and let $\vv_2$ be a direction vector along $L_2$. | Let $\vv_1$ be a direction vector along $L_1$, and let $\vv_2$ be a direction vector along $L_2$. | ||
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| + | {{ : | ||
| The shortest distance from $L_1$ and $L_2$ is measured along the direction orthogonal to both $\vv_1$ and $\vv_2$, namely the direction of $\nn=\vv_1\times\vv_2$. | The shortest distance from $L_1$ and $L_2$ is measured along the direction orthogonal to both $\vv_1$ and $\vv_2$, namely the direction of $\nn=\vv_1\times\vv_2$. | ||
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| Let $\Pi$ be the plane with normal vector $\nn$ which contains $L_1$. | Let $\Pi$ be the plane with normal vector $\nn$ which contains $L_1$. | ||
| - | For any point $B$ in $L_1$, we have | + | {{ : |
| + | |||
| + | For any point $B$ in $L_2$, we have | ||
| \[\dist(L_1, | \[\dist(L_1, | ||
| where $A$ is any point in $\Pi$; for example, we can take $A$ to be any point in $L_2$. | where $A$ is any point in $\Pi$; for example, we can take $A$ to be any point in $L_2$. | ||
lecture_24.1429790587.txt.gz · Last modified: by rupert