Try the (challenge) question below before our next class. For an extra challenge, can you post your solution below using \(\LaTeX\)? (See here for a quick tutorial.)
Find a vector equation of the plane whose Cartesian equation is \(2x+y-z=4\).
11 HL: Planes and Normals
Complete the questions in the PDF file attached before next class. (Questions 1 b) and 3 a) are challenge questions, but you might be able to figure these out using the material we’ve covered in the past few lessons… see the hint below.)
11 HL: Lines & Planes
Complete the following question before our next class.
Find the point of intersection of the line \( \frac{x-2}{5}=\frac{y+2}{2}=\frac{z-1}{3}\) and the plane \(2x-3y+z=0\).
11 HL: The Scalar Triple Product
Complete the question below before our next class.
Exercise 12N.3 question 9
11 HL: The Cross Product
Complete the following questions before our next class.
Exercise 12N.1 questions 1, 4, 8, 10
Exercise 12N.2 questions 3, 4, 5
Exercise 12N.3 questions 2, 5
11 HL: Points of Intersection and Angles Between Lines
Complete the following questions before our next class.
Exercise 13B questions 2, 3, and 4
Exercise 13C question 7
Exercise 13F.2 question 1 abcd
11 HL: Distance for a Point to a Line
Complete the following questions before our next class.
Exercise 13D questions 1ac, 2, 5
11 HL: Vector Equations of Lines in 3D
Complete the following questions before our next class.
Exercise 13A questions 4, 5ac, 6ab
Also, (as a challenge question) can you answer question 2 from class? Both questions are shown below.
- Find the vector equation of the line passing through \(A(1,-1,4)\) and \(B(3,3,-1)\).
- Find the distance of the point \(A(1,2,3)\) to the line given by
\[\vec{r}=\begin{bmatrix}4\\2\\1\end{bmatrix}+\lambda \begin{bmatrix}4\\1\\-1\end{bmatrix}\]
11 HL: Finding Vector Equations of Lines
Complete the following questions before our next class.
Exercise 13A questions 1–3
Also, see if you can finish the question below. (Vector methods not required!) We’ll discuss a vector approach to this sort of question in the lessons to come.
Find the distance of the point \(A(1,3)\) to the line \(y=2x-2\).
11 HL: Vector Equations of Lines
Find a vector equation of the line with Cartesian equation \(\displaystyle{y = \frac{3}{4}x -2}\).