The projection of x onto L becomes x dot our unit vector, times the unit vector, times the unit vector itself.

Some unit vector u.

That is equal to ca dot our unit vector u times unit vector u.

We can define a unit vector that goes straight up in the y direction called unit vector j and once again the magnitude of unit vector j is equal to 1

Times the unit vector itself, so that we actually get a vector.

So that is our j unit vector.

You start with a unit vector there.

Let's say someone gives you a vector v that isn't a unit vector.

Where this is a unit vector version of your vector v up there.

The vector 1, 0 dot the unit vector u, which is just u1, u2.

You can define some unit vector right here.

My unit vector, let's just assume that u can be rewritten as my unit vector is equal to sum u1 and u2.

I showed you this in the unit vector video.

And then, all of that times our unit vector.

Plus b dot u times our unit vector u.

We're going to have that times my unit vector.

0, 1 dot my unit vector dot u1, u2.

The unit vector is this, 1 over the square root of 5 times our vector v.

And what a unit vector is, so the i hat vector goes in the positive x direction.

So, plus sin(t 2) times the j unit vector.

How can you define a line using some unit vector.

As x dot some unit vector that defines our line.

And all that is being multiplied by the j unit vector.

So it's capital P of xy times the unit vector i.

Let's call it u, and I'll say it's a unit vector.

I'm going to multiply that times my unit vector, times u1, u2.

So I'm going to get u2 times my unit vector, u1, u2.

What we can first do is convert v into a unit vector.

So we have U1, which is a unit vector. It has length 1.

Thus, the coordinates of the stress vector formula_2 on a plane with normal unit vector formula_3 passing through a given point formula_4 is represented by formula_5And knowing that formula_3 is a unit vector we have math n_1 2 n_2 2 n_3 2 frac T_1

You can construct a unit vector that goes in the same direction as any vector, essentially just by dividing, or I guess multiplying, that vector times 1 over its length.

Our vector u, our unit vector that defines this line, is equal to the vector 2 over the square root of 5 and 1 over the square root of 5.

The way you turn him into a unit vector, you figure out the magnitude.

If we assume that we're dealing with the unit vector definition for the line.

I need to take this dot my unit vector, let me write this down.

The definition of our projection is you dot this guy with our unit vector.

We can convert v into a unit vector that goes in the same direction.

If you distribute the r, you get exactly r cosine theta as a function of t times our i unit vector plus our sine theta as a function of t times the j unit vector.

So the vector i hat, so that right there is a picture of the vector i hat we put a hat on top of i to show that it's a unit vector.

Of unit vectors. so by definition we introduce the vector i, the vector i, sometimes its called i hat, and I'll draw it like here.

There is no j component, so if you have to visualize this vector field, all of the vectors, they're all multiples of the i unit vector.

You say, hey Sal, how do we know if this is a unit vector or not.

This is equal to, by our definition, we'll use the unit vector version, because it's simpler.

Let me draw it with a little hat to show that it is a unit vector.

That's just how its defined and we also, unit vector tells us that its magnitude is one.