Differences

This shows you the differences between two versions of the page.

--- lecture_20_slides [2016/04/13 15:41] – [Example 2] rupert
+++ lecture_20_slides [2016/04/13 15:43] (current) – rupert
@@ Line 174: / Line 174: @@
 ==== ====
   * $\Pi$ contains $L:\c xyz=\c{6/5}{1/5}0+t\c{-3/5}{7/5}1$, $t\in\mathbb{R}$, orthogonal to $\Pi_3: 2x+y+z=3$
-  * $5\c{-\tfrac35}{\tfrac75}1=\c{-3}75$ is a vector along $L$, so in $\Pi$
+  * $5\c{-3/5}{7/5}1=\c{-3}75$ is a vector along $L$, so in $\Pi$
   * $\Pi_3$ has  normal vector $\nn_3=\c211$, which is in $\Pi$.
   * Normal vector for $\Pi$: $\nn=\c211\times\c{-3}75 = \cp211{-3}75=\c{-2}{-13}{17}$
   * $\Pi$ has equation $-2x-13y+17z=d$
+==== ====
+  * $\Pi$ has equation $-2x-13y+17z=d$ and contains $L:\c xyz=\c{6/5}{1/5}0+t\c{-3/5}{7/5}1$, $t\in\mathbb{R}$
   * Take $t=2$: $(0,3,2)$ in $L$, so in $\Pi$
   * Sub in: $d=0-13(3)+17(2)=-39+34=-5$
   * Answer: $-2x-13y+17z=-5$, or $2x+13y-17z=5$.