1. Precalculus
8-2 Algebraic Vectors
Vectors can be used algebraically using _______________________________________.
• For example, 〈3, 4〉 can represent a vector in standard position, with the
__________________ point at the origin and the terminal point at ____________.
Magnitude can be found using the ___________________________________________.
• Drawing the horizontal and vertical ____________________ of the vector yields
a ________________________________.
• For example, the magnitude of 〈3, 4〉 is ______________________.
Representing a Vector as an Ordered Pair
Initial: P1(x1, y1)
Terminal: P2(x2, y2)
• The ordered pair representing P1P2 is ________________________
• Its magnitude |P1P2| = (x2 − ξ1 )2 + ( ψ − ψ )2
2 1
Example: Write the ordered pair that represents the vector from X(-3, 5) to Y(4, -2).
Then find the magnitude of XY.
Vector Operations
• Addition: _________________________________________________________
r r r
Example: m = 〈5, -7〉 n = 〈0, 4〉, and p = 〈-1, 3〉
r r
Find m + p
• Subtraction: _______________________________________________________
r r
Example: Find m – n
• Scalar Multiplication: ________________________________________________
r r r r
Examples: Find 7 p Find 2 m + 3 n – p

2. A vector that has a magnitude of one is called a _________________________________.
• The unit vector in the direction of the _______________________________ is
always represented _______. It has the coordinates _____________.
• The unit vector in the direction of the positive _____________ is always
represented ______. It has the coordinates ______________.
r
Any vector a = α1 , α2 can be expressed as a _______________ of unit vectors.
r
Proof: a = α1 + α2 
ι ϕ
Note: The _____________ vector, which has coordinates ___________, is denoted ____.
Examples:
Write AB as the sum of unit vectors for A(4, -1) and B(6, 2).
Write DE as the sum of unit vectors for D(2, -7) and E(-1, 5).
HW p. 497 (14 – 40 even)