**Readings Questions:**

You should read the section before
attempting any reading questions or problems. Remember that you are responsible
for all definitions and examples. **Also remember to keep the answers
to the reading questions on a separate piece of paper; these will be randomly
collected from time to time.**

1) Prove definition 1.8.1 makes sense by answering the following.

a) Show that points satisfying (x-x)_{0}=^{.}n0form a plane and that x_{0 }is in this plane. Recall the definition of a plane from page 11.b) Show that

nis perpendicular to this plane (ie show that for any vectorvin this plane,nis perpendicular tov).

2) What is definition
1.8.1 analogous to in ,
that is if the vectors **n** and **x _{0}**
are in ,
what is

{ x | (

3) Consider definition
1.8.2. Prove this is the line through ** **x_{0}which
is parallel to **m** by answering the following.

a) Show that x_{0}is a member of the defined sets of points: { x | x = t_{ }m + x_{0}, t }

b) Show that the line formed by the above set of points is parallel tom(ie show that for any vectorvlying in this line,mis parallel tov).

4) Let **a**
and **b** be two linearly independent vectors and let
x_{0} be a given point. Consider equation (1.8.9):

**Problems:**

**page 75
1, 2, 4, 8, 9, 11, 17, 23, 24, 29**