Category: Mathematics

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