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--- lecture_23_slides [2017/04/24 11:27] – [Skew lines in $\mathbb{R}^3$] rupert
+++ lecture_23_slides [2017/04/24 11:30] (current) – [Example using $\def\dist{\text{dist}}\dist(B,L)=\frac{\|\vec{AB}\times\vv\|}{\|\vv\|}$] rupert
@@ Line 23: / Line 23: @@
-==== Example using $\def\dist{\text{dist}}\dist(B,L)=\frac{\|\vec{AB}\times\vv\|}{\|\vv\|}$ ====
+==== Example using $\def\vv{\vec v}\def\dist{\text{dist}}\dist(B,L)=\frac{\|\vec{AB}\times\vv\|}{\|\vv\|}$ ====
 Find the distance from the point $B=(1,2,3)$ to the line \[L:\c xyz=\c10{-1}+t\c41{-5},\quad t\in\mathbb{R}.\]
@@ Line 59: / Line 59: @@
 ==== ====
-  * Let $\Pi$ = plane with normal vector $\nn$ which contains $L_1$.{{ :sl2.png?nolink&700 |}}
+  * Let $\Pi$ = plane with normal vector $\nn$ which contains $L_1$.{{ :sl2.png?nolink&800 |}}
   * Let $B$ be in $L_2$, and $A$ in $\Pi$ (e.g. any $A$ in $L_1$)
   * Then $\dist(L_1,L_2)=\dist(B,\Pi) = \frac{|\vec{AB}\cdot \nn|}{\|\nn\|}$
@@ Line 75: / Line 75: @@
 ==== Distance between lines in $\mathbb{R}^3$ in general ====
-  * The formula $\dist(L_1,L_2)=\frac{|\vec{AB}\cdot \nn|}{\|\nn\|}$ where $\nn=\vec v_1\times vec v_2$ works for
+  * The formula $\dist(L_1,L_2)=\frac{|\vec{AB}\cdot \nn|}{\|\nn\|}$ where $\nn=\vec v_1\times \vec v_2$ works for
     * skew lines (not parallel, not intersecting)
     * actually: any non-parallel lines $L_1$, $L_2$
@@ Line 82: / Line 82: @@
     * Instead: observe that $\dist(L_1,L_2)=\dist(A,L_2)$ for any point $A$ in $L_1$
     * So we can use one of of the point-to-line distance formulae we saw earlier.
+==== End of the course ====
+  * Next time: some examples from the most recent exam paper
+  * Have a look at these before Thursday's lecture to prepare