VECTORS

- Vectors have a size, or magnitude, and a direction. They are usually represented by an arrow with a length scaled to the magnitude and the arrow pointing in the direction.

- Scalars have only magnitude.
- Examples of vectors are: displacement, velocity, and acceleration
- Examples of scalars are mass and speed.

- Vectors can be added using a graphical method.
- Vectors can be added using components.

A. A unit vector is a vector that is 1 unit long and points in the specified direction.

B. The unit vectors: **i - **points along the x-axis in the positive x-direction; **j** - points along the y-axis in the positive y-direction; **k** - points along the z-axis in the positive z-direction.

C. For the vector **A**

Here **A** = A_{x}**i** + A_{y}**j**

A_{x }= Acosq and A_{y} = Asinq

Note that A^{2} = A_{x}^{2} + A_{y}^{2} and that tanq = A_{y}/ A_{x}

D. If we have a second vector **B** that makes an angle of b with the x-axis, then we can write that the vector **C** is the vector sum of **A** and **B.**

**C** = **A** + **B**

C_{x}**i** + C_{y}**j** = (A_{x}**i** + A_{y}**j) + (**B_{x}**i** + B_{y}**j)**

C_{x}**i** + C_{y}**j** = (A_{x} + B_{x}**)i + (**A_{y}+ B_{y}**)j**

C_{x} = (A_{x} + B_{x}**) = **Acosq + Bcosb

C_{y} = (A_{y} + B_{y}**) = **Asinq + Bsinb

III. Vectors can also be multiplied, but this will be introduced later in the course.