Vectors are quantities that are specified by both a direction and magnitude of length. The way you draw a vector is by drawing an arrow. This arrow has a length and points in some direction.
When we use vectors we need to introduce the coordinate system. We represent vectors in terms of their components along the coordinate axis. So if we have an arrow we can now communicate with someone else about how much the vector goes in the x direction, the y direction and the z direction. When we have a vector quantity we put an arrow on top of the labeling letter to remind us that it is a vector. It looks like so .
A vector is a combination of unit vectors that are placed along the the coordinate axes. These unit vector have length one. A unit vector is denoted by a lowercase letter with a hat above it, like so, . It is pronounced as a-hat. Our standard correspond to the x-y-z coordinate system. points along the x-axis points along the y-axis and points along the z-axis. We can express any vector in terms of its components relying on the unit vectors. With as any numerical values we can write any vector in the following form . The other notation for a vector
If we have two points in space we can connect them and make it into a vector. example in 2d Another vector is . Vector A is 3 units in the x and y direction and 2 units in the z direction.
If a vector is still a bit abstract to you then think of a compass. The arrow has a certain length, this is our magnitude, and it points in any direction (north, south, east, and west).
- Click here for a graphical introduction to vectors:
- Click here for an algebraic introduction to vectors:
- Click here for an interactive demonstration: