Before Wednesday's class read Sections 13.2 and 13.3 and be prepared to answer
the following questions. In class you will have the chance to ask
questions about any of the material you're not 110% sure about.
So bring your questions!! Also, try a few
homework problems to see that you've understood the reading.
Before Friday's class do the same for Section 13.4.
(1) What is the physical/geometrical definition of a vector?
(2) What is the algebraic definition of vector?
(3) When are two vectors equal?
(4) What's the point of the discussion in the book about
the "representation" of a vector and about the "position vector"?
(5) What's the length of the vector <1,2,3>?
(6) Explain both algebraically and geometrically how you
add and subtract two vectors and what scalar multiplication
is.
(7) How do you convert from the geometric to the algebraic
descriptions of a vector, and vice-versa?
(1) What is the algebraic definition of the dot product between two vectors?
(2) What sort of quantity is the dot product of two vectors?
(3) What is <3,4>.<5,6>? What is i.j?
(4) How is the dot product related to the length of a vector?
(5) What is the physical/gemetric definition of the dot product?
(6) What is the angle between the vectors <1,2,3> and <4,5,6>?
(7) Note: We will omit the material on Direction cosines and angles
as it is not used in the rest of the course.
(8) How would you test if two vectors are perpendicular?
(9) I will be looking for a volunteer to prove Theorem 3 at the board
using 1 picture and 3 equations.
(10)
Calculate the projection of the vector <3,4,5> onto the vector <2,0,0>.
(The answer should be a vector).
(11) I will be looking for volunteers to (a) explain what
the projection formula means and (b) how to prove it.
(1) What sort of quantity is the cross product of two vectors?
(2) What is the physical/geometrical definition of the cross product?
(3) What is 3i x 4j?
(3) What is the algebraic definition of the cross product in terms
of determinants?
(4) Do Section 13.4 #2
(5) Give a one sentence proof of why the cross product of two vectors
is perpendicular to both of them.
(6) How (and why) is the cross product of two vectors related to their
dot product?
(7) How and why is the cross product related to the area of a triangle?
(8) What is the formula for the volume of a parallelipiped and why is
it true?
Last modified Sept 1st, 2003