 You might recall us discussing a vector as multiple pieces of information describing one entity. For example, in this picture above, we had three pieces of information, an age, a weight, and a heart rate in beats per minute, all describing one person, but all represented in physical space with a particular point drawn in three-dimensional space to represent the three dimensions of the information. Well, another way to describe a location in space is to use a graphical vector. And by that, I mean to describe any location in space, we can actually draw, and point to it by drawing an arrow from some origin. So if we have some location perhaps in space, we create some basis, some origin, some starting point, and then we draw an arrow that points to it, and this is a graphical vector. If we wish to identify a vector in space, either two-dimensional or three-dimensional space, we'll need a graphical reference basis and either two or three spatial components. Spatial components being measurements of something in space. Some typical reference bases are first of all what we would call a Cartesian basis. In a Cartesian basis, you have two or three perpendicular axes. In your algebra class, you work with two of them, your x and y axis, or maybe later on, you add a third axis, trying to draw it so that it's in the page, but in this case, they're all perpendicular to each other. Three perpendicular axes make up this basis, and then you would have three component lengths, which each of those component lengths being parallel to each axis. So you would have lengths to consider along your horizontal axis, lengths to consider along your vertical axis, and lengths to consider along the axis that goes into or out of the page. That would be a Cartesian basis and the three components associated with it. You can also have a cylindrical basis. Our reference for a cylindrical basis consists of a reference plane with a reference axis inside that plane. A reference plane and a reference axis in the plane. And then our components are a direction as defined by an angle within the plane, some sort of angle inside the plane. A length, is there an angle in the plane, a length in that direction, and then in 3D our third component is a vertical length out of the plane. The three of those together define a location in space and a vector in a cylindrical basis. And a third common type of basis is a spherical basis. In the spherical basis again you need a reference axis inside a reference plane, as in the cylindrical basis. Reference plane with a reference axis inside. But our components in this case are slightly different. Our first component is similar to the first one. It's an angle in the plane, which gives us some sort of direction inside the plane. But our second component is an angle out of the plane. Sometimes this angle is defined up from the plane. Sometimes the angle is defined down from a vertical axis perpendicular to the plane. In this case I'll draw it coming up from the plane. Basically establishes a direction both in above a portion of the plane and then out of the plane. And then our third and final piece is a length along those directions. Three different types of bases in 3D and each of them requires three pieces of information. In the first case you need three lengths. In the second case you need one direction, an angle giving a direction and two lengths. In the third case you need two angles to define direction and one length. So in general a graphical vector has a magnitude. And you've heard this before in discussions of vectors. It has a magnitude and a direction. Where a magnitude is a length in the space it's visualized in and a direction is an orientation within this visual space whether it's two dimensions or three dimensions. However, if we're trying to compare a graphical vector to an information vector the measures of these particular value may not have a sensible physical meaning if you have a basis that's kind of composed of mixed units. For example, if I consider a physical space but I use number lines to establish information in that space and my space along my x-axis is going to represent an age and years and my space along the y-axis represents a weight in pounds I can represent some information. There is a vector that represents this information for one person, one entity, somebody who is 47 years old and weighs 203 pounds. However, if I draw a graphical vector to represent this information it does have a magnitude and it does have a direction in this space we've drawn it in but those things don't really have a physical meaning. For example, what would the units be of that magnitude? Some combination of years and pounds which we can find mathematically but don't really have a physical meaning. However, some physical concepts have a spatial component. In other words, they have some measurement in actual space and they can be described with a magnitude and a direction. For example, relative location. If I'm a person and I'm trying to find a treasure indicated by some sort of treasure mark the information about the direction to travel to get the treasure and how far I have to go to get there makes sense to represent with a graphical vector because it has a spatial component. I might have to travel 20 yards in a direction that is 30 degrees north of east or if I'm an airplane flying through space I might be traveling in a direction that's 10 degrees well that has a pitch of 10 degrees or an elevation of 10 degrees that's 400 miles per hour. In that case, that's the velocity which has a spatial component and makes sense to be represented by a graphical vector. A third one, say I'm somebody in a parachute I am concerned about the forces that are acting on me. For example, there is my weight which might be negative 100 Newton but I would also be concerned about whether the drag force holding me back was balancing that out and keeping me at a constant hopefully slow velocity and those forces on me have a spatial component their direction and magnitude have a meaning that makes a lot of sense when represented with a graphical vector. To recap, both the information on what a vector is and on graphical vectors. First of all, the scalar value is some value represented with a number and a unit. Without your unit, your number is meaningless. A vector is a family of associated scalar values and in order for a vector to make sense to be communicated to somebody else you would need to express it as components one component per dimension in a basis and we should recognize that there are multiple representations for a single vector. The dimension of your vector is the number of scalar values associated together within the vector. A graphical vector is an arrow with magnitude and direction that can be represented using components in a graphical basis.