Announcements
• Final exam 12/16. Times posted in WebCT.
• Email me ASAP if you need to change time.
• Old labs available - December 11 for make-up.
Labs accessible in 213 Armstrong.
• Old HW - December 16. Accessible from
anywhere.
• Last new lab will be December 9. “Bonus” points.
• Miss a test? Makeup Wednesday December 7.
Email me to arrange a time.
• Evaluation, review in class next Wednesday
Q
Terminal
Point
Initial
Point
P
Directed line segment
Terminal
point of w
vw
Initial point
of v
v
w
Vector addition is commutative.
vwwv
Vector addition is associative.
u  v  w   u  v   w
v00v  v
v   v   0
v
2v
v
Use the vectors illustrated below to graph
each expression.
w
v
u
v
w
vw
2v
w
v
w
2v and - w
w
2v
2v  w
If v is a vector, we use the symbol v to
represent the magnitude of v.
A vector u for which u  1 is called a
unit vector.
Vector magnitude is like complex
number (1) real part (2) imaginary part
(3) argument (4) modulus
Let i denote a unit vector whose
direction is along the positive x-axis;
let j denote a unit vector whose
direction is along the positive y-axis.
If v is a vector with initial point at the
origin O and terminal point at
P = (a, b), then
v  ai  bj
P = (a, b)
b
bj
ai
a
Find the position v ector of the vector

v  P1 P2 if P1   2,1 and P2  3,4.
v  x2  x1 i   y2  y1 j
P2  3,4
P1   2,1
O
5,3
If v  3i  2 j and w  4i  j, find
2v  3w
If v  3i  2 j, find v
(1)4
(2) 5
(3) 13
(4)5
Theorem Unit Vector in Direction of v
For any nonzero vector v, the vector
v
u
v
is a unit vector that has the same
direction as v.
Find a unit vector in the same
direction as v = 3i - 5j.