Category: 11 Mathematics HL

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11 HL Limits

Complete the following before our next class.

Exercise 17A questions 1, 2c, 3, 5ai
Exercise 17B.1 question 2
Exercise 17B.2 question 1

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11 HL Planes and Matrices

  1. Use row reduction to express the matrix below in row echelon form (or reduced row echelon form).
    \[\left[\begin{array}{@{}ccc|c@{}}
    1 & 3 & -2 & 4 \\
    -2 & -6 & 4 & 9 \\
    2 & 1 & 1 & -2
    \end{array}\right]\]
  2. Use row reduction to express the matrix below in row echelon form (or reduced row echelon form).
    \[\left[\begin{array}{@{}ccc|c@{}}
    1 & 3 & -2 & 4 \\
    -2 & -6 & 4 & 8 \\
    2 & 1 & 1 & -2
    \end{array}\right]\]
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11 HL Vectors Assignment [updated]

Complete the questions here and submit your work to me as an electronic file before the end of the day on Monday, February 5th.

You can use any software you like to create your file, but your submission should be sent to me as a PDF document.

Update: Are you trying to use Google Docs for this? Surprisingly, the Google Docs equation editor doesn’t support vectors (or matrices)! If you don’t have \(\LaTeX\), Word, Or Pages available, you could also use LibreOffice (which is free and has an equation editor). If you can’t find an alternative, handwritten work (hard copies) will be accepted.

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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.

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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 \(L_3\).

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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.