hello class Professor Anderson here let's talk about unit vectors this is a way to uh describe vectors in cartisian coordinate space and a unit Vector is a dimensionless vector okay there's no units associated with it and it has a magnitude equal to one and that's why it's called a unit vectors one unit all right so the only thing that unit vectors do is they specify Direction They specify the direction that you're moving now in our cartisian coordinate system we said we have X we have we have y we have Z and so we'd like to identify unit vectors that correspond to the x axis the Y AIS and the Z axis and the ones that we choose are i j and k we write them as I hat J hat and K hat and the the Hat this thing is called a hat it means it is a unit Vector so it is a vector but it only has magnitude one all right so anytime you're along the x axis you're going to use an I hat anytime you're along the y- axis you're going to use a j hat so let's draw a coordinate system and let's try the following I'm gonna give you a point right here let's say that that is0 five four okay it is five out in the X Direction one two three four five it is four up in the y direction so let me ask you the following question how do I write that vector and let's call it Vector a how do I write that in terms of unit vectors and if somebody knows just raise your hand and Shout It Out no I just had a scratch how do I write the vector a in terms of unit vectors any thoughts I'll do the hard part for you okay two Dimensions there's something that's going to go in front of the IH hat there's something else that's going to go in front of the J hat what do you think a subx and a sub y a subx and a sub y that sounds fantastic and in fact for the problem that we just identified can we say exactly what those a sub x's and those a sub y's are so what what would you write what was what's the next line I should put um as subx I would go along the X AIS good so we need to figure out how long this is how long is it oh five five five I have if that one's five what does the other one have to be four four okay that's what this Vector is that's how you write it five I plus four J hat and what it means is let's move five units in the X Direction that's what the I hat means and let's move four units in the y axis Direction which is the J hat okay that's what those two things mean and that is this Vector right here it starts at the origin and it goes up to that point five comma four okay everybody okay with that so far all right good [Music]