LHE 11.1 Vectors in the Plane Calculus III September 10, 2009 Berkley High School

Definition of Vectors A vector is an object having both a magnitude and a direction.

Notation P is at the “tail” or “initial point” Q is at the “head” or “terminal point” Q P

Notation We will use the notation with the arrow over the vector’s name. The book uses a bold letter to signify a vector, but it is difficult to do this in your notes. Q P

Operations with vectors

Vectors in Component Notation Because vectors can be moved anywhere without changing, a vector, we can think about the vector as the location of the head of the vector when the tail is on the origin. Although it looks like a coordinate, we use different notation:

Vectors in Component Notation

Vectors in Component Notation

Vectors in Component Notation

Definitions Zero vector: vector with magnitude 0

Notation

Scalar Multiplication Scalars are real numbers, not vectors

Operations with vectors

Unit vectors Unit vectors are vectors with magnitude=1 Any vector (with the exception of the zero vector) can be transformed into a unit vector.

Special Unit Vectors

Rewriting component form

Converting from polar form

Vectors on the TI-89 Use NewProb before starting (in the F6 menu) [5,2]→u (Square brackets, not parenthesis) 2u unitV(u) (Math:Matrix:Vector Ops:UnitV)

Assignment Section 11.1, 1-17 odd, 23-57 odd