Category: 11 Mathematics HL

Complete the following questions before our next class.

Exercise 15H.2 questions 1fg, 2
Exercise 15I 9, 10, 11a, 12, 13

 

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 \(L_3\).

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.

Complete the following questions on lines in 3D (some of which involve the Cartesian equation of a line in 3D) before our next class.

Exercise 15C questions 5bcd, 6d, 7abc, 8, 10

Complete the following questions before tomorrow’s lesson.

Exercise 15C questions 1–4

Complete the following questions before our next class.

Exercise 15A questions 2, 4, and 5

Complete the following questions for our next lesson.

Exercise 14H questions 9a, 11
Exercise 14I questions 8, 11ac
Exercise 14J questions 4, 12ab, 17, 18, 20

Here is the (long) list of questions we were working on today. Try to have most of these completed before our lesson tomorrow (note that no additional questions were added to the list).