 Now, let's look at vector scalar multiplication. If we're talking just normal multiplication, that's scalar multiplication. Both values are scalars, meaning neither one of them has a direction. We're used to seeing this in terms of pure numbers, things like 2 times 3 equals 6. But in physics, there can also be physical quantities, which are numbers in a unit. So for example, the area is 3 meters times 2 meters, giving us 6 meters squared. Well, if I've got a vector and a scalar, and I'm multiplying them, that means that one of those two values, the vector, has a direction associated with it. So I could express this as c times a or ca. Now, no, we tend not to put the little x as a multiplication sign in physics, because x is often used for our position variable. When I do this kind of vector scalar multiplication, the rules are that the magnitudes multiply, but the direction stays the same. So both our numbers c and our vector a have a magnitude, and those two things are going to multiply. Here's a few examples. So this one over here on the left, I can imagine that the original arrow here is my original vector a. And that means that this represents 3 times a, or it's 3 times as long, but keeps the same direction. I can do it with fractions, though, too. This one is 1 and 1 half times as long as the original vector a. Now, if I'm going to do it by components, not graphically, then each one of the components of the vector is multiplied through by whatever scalar number I've got. So if I've got a scalar times a vector, then the scalar times the x component of the vector and the scalar times the y component of the vector give us our resulting x and y components. As an example, let's say our scalar was just the number 2 and our vector was 3 and minus 1 for its two components. Well, then the x component is our 2 times 3, giving us 6, and the y component is 2 times our negative 1 or negative 2. So our result is 6 for the x component and minus 2 for the y component. If I'm using my i, j, k equations to represent the vector, then the number is just multiplied through. So for example, let's say my vector was written out here as an equation, minus 4 i hat plus 2 j hat. And again, your minus 4 is the x component of the vector. Your 2 is your y component of the vector. And let's say that I've got a constant scalar of just 2.5. Well, then when I multiply that through, the 2.5 distributes to the equation so that each one of the terms has the 2.5 multiplied in there. So that would simplify down to minus 10 i hat plus 5 j hat. Division works exactly the same as multiplication. The amount you're dividing by just sort of distributes through your equation. So each component, x and y, are divided by that same number of whatever your original equation was divided by. So this is how we deal with vector scalar multiplication. Now the numerical examples I gave you didn't have units, but just keep in mind, just like our regular multiplication. If there were units on those scalars and vectors, not only does the number multiply through, but the units are going to multiply through as well.