11 HL Vectors Test

We’ll have our test on all the vectors material on Tuesday, February 13th.

The best resource to use in preparing for the test is the set of questions that has been distributed to you via email. If you have any questions about the solutions, we can discuss some of these in our classes leading up towards the test.

11 HL Lines in 3D

Consider the three lines defined below.

\[L_1: \vec{r}=\begin{bmatrix}1\\2\\3\end{bmatrix}+\lambda \begin{bmatrix}1\\-3\\-4\end{bmatrix}\]

\[L_2: \vec{r}=\begin{bmatrix}-2\\-3\\0\end{bmatrix}+\lambda \begin{bmatrix}4\\4\\0\end{bmatrix}\]

\[L_3: \vec{r}=\begin{bmatrix}2\\-5\\-3\end{bmatrix}+\lambda \begin{bmatrix}0\\2\\1\end{bmatrix}\]

Show that \(L_1\) and \(L_2\) are skew lines, then find the point of intersection of \(L_1\) and \(L_3\).

\(\LaTeX\) and Selected Topics in Mathematics

If you’re unfamiliar with  \(\LaTeX\), it’s the system I use to create the slides and tests in our courses. It’s also used to enter mathematical expressions on this site (and many others).

By request I’ll be running some tutorials in \(\LaTeX\) on Mondays after school (usually these will be held in my classroom, but for the first week it’ll be in 122). It would be useful to know if you’re writing a math-heavy extended essay (in mathematics or one of the sciences, for example), and would also be useful for your mathematical exploration.

After we’ve finished looking at  \(\LaTeX\), we can look at some additional topics in mathematics, with topics selected based on interest (these could include things that typically fall outside the scope of the IB Mathematics courses, like linear algebra, logic, set theory, abstract algebra, or analysis).

If you’re interested in getting started with  \(\LaTeX\), I recommend that you install a full version of  \(\LaTeX\) on your computer—I’ve added instructions for installation here.

11 HL Planes

Here are a couple of short questions to look at before our next lesson.

  1. Verify that the points \(A(1,2,3)\), \(B(-2,0,0)\), and \(C(3,-2,-1)\) are not collinear.
  2. Find the vector equation of the plane that contains all three points from question 1.
  3. Find the Cartesian equation of the plane you determined in question 2.
  4. Verify your answers using GeoGebra.