Chapter 3: Vectors and Coordinate Systems

Vector

A quantity having both a direction and size(magnitude)

Scalar

A quantity that is fully described by a single number(with units). m will represent mass, T temperature, V volume, E energy, and so on. These are all scalars

A Conventional xy-Coordinate System and Quadrants

Be sure to label your axes by placing x and y labels at the positive ends of the axes so as to (1) identify which axis is which and (2) to identify the positive ends of the axes

Component Vectors and Decomposition or Vectors

Once the directions of the axes are known, we can define two new vectors parallel to the axes that we call *component vectors*

Velocity Vector

The absolute value of the velocity vector is the object's speed and is the magnitude of the vector which is a scalar.

Displacement Vector

The displacement vector is a straight-line connection from his initial to his final position, not necessarily his actual path

Magnitude of Vector

The size of a vector is *magnitude* so we can also say that a vector has a direction and magnitude

Net Displacement

The sum of two vectors is called the *resultant vector*. Vector addition is cummutative

Graphical Addition

The tip-to-tail method for adding vectors, which is used to find net displacement. Any two vectors of the same type can be added in this way

Equal Vectors

Two vectors are equal if they have the same magnitude and direction

Unit Vectors

Vectors with magnitude of 1, has no units, and are parallel to a coordinate axis

Vector Addition by Algebraic Addition

We can perform vector addition by adding x-componenets of the individual vectors to five the x-component oor the resultant and by adding the y-components of the individual vectors to give the y-component of the resultant