UNIT 1 VECTORS

SECTION 1.1 VECTOR CONCEPTS

A vector is a mathematical object with both MAGNITUDE (size) and DIRECTION

Quantities that can be represented by a single number are called SCALARS

Initial point (tail) Terminal point (tip) Vectors can be represented Geometrically as a Directed Line Segment

They can be represented Algebraically by ordered pairs or triples (a, b)(a, b, c)

Various symbols can be used to represent vectors

The Magnitude (size) of a vector is denoted by

The opposite of vector AB is the vector BA. It has the same magnitude but the opposite direction AB BA

EQUALITY OF VECTORS Two vectors AB and CD are equal if and only if: AB is parallel to CD AB has the same magnitude (size) as CD The direction from A to B is the same as from C to D

The zero vector is represented by 0. Its magnitude is zero and its direction is undefined.

The angle between two vectors is the angle(  180°) formed when vectors are placed tail to tail.  u v

A unit vector in the direction of any vector can be found by dividing by its magnitude | | A unit vector is a vector with a MAGNITUDE equal to one

Any unit vector or Any vector

Example 1: Examine the vectors in the diagram. a)Express b and c as a scalar multiple of a b)Express a, b, and c in terms of the unit vector a c b

a c b

Homework: page 8 # 1-12,