Vectors

A vector is a quantity that describes both magnitude and direction.

Vector Types

Unit Vector

Magnitude of vector is 1. Denoted by $\hat{v}$

Vector Relationships

Equal Vectors

2 vectors are equal if they have the same magnitude and direction $\vec{u}=\vec{v}$

Opposite Vectors

Same magnitude, different direction $\vec{u}=-\vec{v}$

Colinear Vectors

2 vectors are going in the same direction but have different scalars. $\vec{u}=k\vec{v}$

Co-planar Vectors

2 Vectors lie on the same plane. You can write one vector as a linear combination of the other 2. $\vec{a},\vec{b}ϵ\vec{c}$ $\vec{c}=s\vec{a}+t\vec{b}$

Perpendicular Vectors

Vector Concepts

• Vector Addition
• Vector Subtraction
• Vector Scalar Multiplication
• Vector Magnitude
• Component Vector Operations
• Turning Vectors Into Unit Vectors
• Spanning Set

2D Vectors

Represented by $\overrightarrow{[x,y]}$

Standard Unit Vectors

• $i=\overrightarrow{[1,0]}$
• $j=\overrightarrow{[0,1]}$

Special Vector Types

• 2D Position Vector
• 2D Direction Vector

3D Vectors

Represented by $\overrightarrow{[x,y,z]}$

Standard Unit Vectors

• $i=\overrightarrow{[1,0,0]}$
• $j=\overrightarrow{[0,1,0]}$
• $k=\overrightarrow{[0,0,1]}$