Vectors and Operations

Notation

Notation is important: When you use lower case notation you imply that the vector is starting at the Origin. This means that the vector components are the same as the co-ordinates of the end point:

Vectors in the Plane

Base Unit Vectors

Base Unit Vectors i, j and k are vectors of 1 unit length, in the direction of the x-axis, the y-axis and the z-axis respectively. The Point P below has position vector p = xi + yj.

Unit Vectors

Unit vectors are vectors that have a magnitude of 1 unit. They don't necessarily have to be base unit vectors. You can make any vector a unit vector by dividing it by it's own magnitude.

About the videos by PatrickJMT: Patrick uses alternative notation for his vectors:

http://youtube.com/watch?v=6o_S7u7Ddx4

Position Vector

This is a name given to a vector ending in a point B, relative to another point A (which is the start of the vector).  If no reference is given it can be helpful to assume the origin to be the reference. The lowercase notation implies this.

The position vector of B relative to A is: 

Vector Addition and Subtraction

Vectors have a magnitude and a direction. They can be added and subtracted. Play around with it:

This video shows what Vectors are, how to draw them and how to add them together.

http://youtube.com/watch?v=pimr9I92GZY

The Vector between two Points

This Video shows how Vectors tie in with the coordinate system that we already know (Cartesian Plane). Keep in mind that we will soon go 3D with this...

http://youtube.com/watch?v=60btq9PN8IM