PX153 - A1 - notation and geometrical representation

scalar

a scalar quantity is defined by its magnitude
independent of coordinate system
eg: density, speed

vector

has a magnitude and direction
components depend on the coordinate system
geometrically, it's an arrow, length proportional to the magnitude
for vectors, in books, often in bold v
often underlined / with an arrow on top
magnitude is given by :

v = | \vec{v} | = \sqrt{v_{x}^{2} + v_{y}^{2} + v_{z}^{2}}

direction is often described by a unit vector (underlined with a hat on top)

\underset{―}{\hat{v}} = \frac{\vec{v}}{| \vec{v} |}

any vector can be written as:

\vec{v} = v \underset{―}{\hat{v}}

vector fields

describes a vector that varies continuously in space
eg: wind - has a magnitude (speed) and a direction that vary continuously with position