## MAT B41 — Week 1

Posted in 2018 -- MAT B41, Lecture Notes, Uncategorized by pgadey on 2018/05/08
First class tonight. Come on out! Tutorials next week. The Pre-Course Survey is available here.

Suggested Exercises:

• Section 1.1 Vectors in Two- and Three-Dimensional Space: 1, 4, 7, 10, 11, 13, 15, 25, 27, 28
• Section 1.2 The Inner Product, Length, and Distance: 1, 6, 7, 8, 15, 19, 25

Past Term Tests:

2016 Term Test: Let $\ell_1$ be the line through $(0,1,1)$ and $(-1,2,1)$; let $\pi$ be the plane through $(0,1,1)$, $(0,1,0)$, and $(-2,-1,-1)$; and let $\ell_2$ be the line orthogonal to $\pi$ and passing through $(4,0,1)$.

1. Give both a normal form equation for $\pi$ and a parametric description for $\pi$.
2. Give parametric descriptions for the lines $\ell_1$ and $\ell_2$.
3. Determine whether the line $\ell_2$ meets the plane $\pi$.
4. Determine whether there is a plane containing the lines $\ell_1$ and $\ell_2$. If there is a plane, find its equation.

2015 Term Test: Let $\pi$ be the plane through $(-1,0,2)$, $(1,3,1)$, and $(2,1,-1)$.

1. Give a normal form equation for $\pi$.
2. Give a parametric description of the line $\ell$ through $(0,0,1)$ and orthogonal to $\pi$.
3. Where does $\ell$ meet $\pi$?

Notes:

Parker’s notes might contain more material than covered was covered in lecture. If you take PDF notes of class, please send them to Parker and help the whole class out! You can ask to have your name included or not.

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