Last updated April 10, 2022

Status: Tags: Links: Math 232 Course Outline

Vectors

Principles

Notation of vector written ?

• bolded, or letter with arrow on top

Notation of a vector visually ?

Vectors are equal if ?

• they have same magnitude and direction
• Just same distance travelled, initial position doesn’t matter
• Vector Angles
• Vector Line Equations

Properties

• Vector Length

• Vector Distance

• Orthogonal

• Orthonormal

• Dot Product

• Parallelogram Equality

  • 

• Normal Vector

• Closed Vectors

Opposite vectors

Let v = (1,-2,1). Find a vector u of mag 7 that is in opp direction than v. ?

• Multiply it by length of opp vector over length of vector v
• Negate v $\frac{7}{\sqrt{26}}$(-1, 2, -1)

Let v = (1,-2,1). Find 3 vectors w1; w2; w3 such that w1 is parallel to v1 and such that the set {w1; w2; w3} is an orthonormal set ?

• Find parallel w1 using 1/w1_length and point v
• Think of two other points that would result in orthonormality yoursellfl
• Find length of those, add in relevant fractions

Used in

• Parametric Equations
• Span
• Basis

Operations

• Linear Combinations
• Vector Operations

Backlinks

1

list from Vectors AND !outgoing(Vectors)

References:

Created:: 2022-01-10 13:07