 When we work in fluid mechanics there are a lot of vectors that we're dealing with and consequently what we're going to do here in the next few segments is we're going to do a review of some of the important vector operators that we use when we study fluid mechanics. Okay so when we're studying fluid mechanics the governing equations be it the Navier-Stokes equations or the Euler equations which we'll be looking at as we go through the course. Typically you're dealing with vectors in those equations. They're vector equations and consequently they'll have the different components for whatever vector system you're using be it Cartesian, cylindrical or spherical coordinates. And it's also because we're dealing with velocities and velocities have three components. Once we have our velocity field that we're usually dealing with as well we're dealing with stresses that can occur within the fluid and we also handle the stresses accommodating with these multi-component or vector systems and consequently what we need to do is spend a little bit of time brushing up on those skills because they're very important for the analysis of problems in fluid mechanics. Another point that I should mention is that although we're going to be looking at the Cartesian coordinate system which is quite often used in fluid mechanics depending upon the nature of the problem you could also have where you're dealing with either cylindrical or a spherical coordinate systems and the relations that we're going to look at in the next few segments would be a little different so just be aware that you cannot take the relations from the Cartesian coordinate system and apply them to either cylindrical or spherical you would have to have different things for things like the dot product or the cross product which we'll be looking at. So that's just a bit of a cautionary note and you would want to look that up in books or on the internet to determine how to handle those coordinate systems and again that would depend upon the nature of the problem that you're dealing with. So what we're going to begin with is the the most basic aspects here and we're going to begin with the position vector so this could describe the position of a fluid particle it could also describe a position that we're interested within our coordinate system and so you've probably seen this in your math courses and here we have ijk and those are unit vectors and so if you recall the property of the unit vector was the magnitude of the unit vector is equal to one so if we were to compute the magnitude of any of the unit vectors we would get one and we also deal with things it could be velocity it could be any of the other things we're looking at with fluid mechanics but i'm just going to write it in a generic manner let's say that we have some vector so a and so a is going to have scalar value in the i direction plus scalar value in the j direction plus scalar value in the k direction and just to make it interesting we'll introduce vector b because that will enable us to operate between a and b and b would be defined in the following way and these are just some arbitrary vectors that we're going to deal with so that is where we will stop this segment and what we're going to do next is we're going to go on and we're going to use a and b and sometimes we'll introduce b for velocity but we're going to look at the different operators that you'd be using as you go through analysis of fluid mechanics and so this will be a useful place for you to come back to as as we go through the course if you get confused with any of the vector operators or how we're doing something please do return to these segments and this would then enable you then to proceed as we go through further analysis in the course