ALGEBRAIC VECTORS in R2 and R3
Algebraic vectors are also referred to as Cartesian vectors or analytic vectors.
A.
ALGEBRAIC VECTORS in R2
𝑢 = 𝑂𝑃
position vector
= (𝑎, 𝑏)
called an algebraic vector
with components a and b
MAGNITUDE
𝑢 = 𝑎2 + 𝑏 2
NOTE: 1.
2.
B.
DIRECTION
𝜃 = 𝑡𝑎𝑛−1
𝑎
𝑂𝑃 has its tail at the origin and is therefore called a position vector.
(a,b) can represent a point, P(a,b), or a vector, 𝑢 = (𝑎, 𝑏)
ALGEBRAIC VECTORS in R3
THREE DIMENSIONAL SPACE (R3)




𝑏
3 coordinate axes (x, y, and z)
origin (0,0,0)
ordered triples P(x, y, z)
3 coordinate planes (xy–, xz–, yz–plane)
RIGHT–HANDED SYSTEM of COORDINATES
When the positive x–axis is rotated 90o
counterclockwise it becomes coincident
with the positive y–axis.
Position vectors in R3 can be expressed in
component form:
𝑢 = 𝑂𝑃
= (𝑎, 𝑏, 𝑐)
MAGNITUDE
𝑢 = 𝑎2 + 𝑏 2 + 𝑐 2
C.
EXAMPLES
Ex 
State the coordinates of points A, B, C, D, E, and F in the given diagram.
Ex 
State the location of each of the following points:
a)
(0,–2,0)
b)
(1,–2,0)
c)
(0,1,2)
Homework: p.316–318 #2b, 3, 6–8, 10(don’t illustrate), 12, 13, 15abc, 16, 18, 19