High quantities of phosphorous protein and all that crap.

These two things are equivalent quantities.

Once again, these are vector quantities

And the way that we differentiate between vector and scalar quantities ... ... is that we put little arrows on top of vector quantities.

They use large quantities chloroprene and benzene.

So, you might price the product if you buy in quantities of 1 10 it's 1000, but if you buy in quantities of 10 100 it's 900.

This is a very well known feature in which we perceive quantities in relative ways quantities like the intensity of light or the loudness of a sound.

In the city, large quantities of garbage are being produced every day.

Japan used to trade silk in large quantities.

So ratios are just expressions that compare quantities.

Coal exists in vast quantities, and generates almost half of the planet's electricity.

Foreign products arrived on the market in large quantities.

Smart materials are hard to obtain in small quantities.

Water wings an inch of water.

eyes of well water eyes of dream water.

Those are correlations between two quantities. One of which does not depend on distance.

And these strands of magnetic field inside the superconductor, they come in discrete quantities.

We grow the cells outside the body in large quantities.

Like most thermodynamical quantities, it can be expressed as a function of these two variables.

The water of the water supply is dangerous.

0.3 of all fresh water is surface water.

And we are going to combine these quantities together as follows.

We're just adding or subtracting the same quantities on both sides.

They were reasonable portions of protein served with copious quantities of vegetables and small amounts of starch, usually rice.

And when the sun shines, you get copious quantities of these things, called neutrinos, pouring out.

Yeah, every single cell in us can produce minute quantities of hydrogen sulfide in great crises.

Gaga gaga gaga guga guga guga wada gaga gaga guga gaga wader guga guga water water water water water water water water water.

These are just scalar quantities, and we saw that the dot product is associative with respect to scalar quantities, so we can just change the order here.

There's plenty of water.

A lot of water.

With this new equation we can just plug in the known quantities.

If i wanted to write an analogous thing for the scalar quantities ... ...

Or, I guess order these quantities however you want to do it

I'm just These are all just expressions that are comparing two quantities.

For quantities of 20 or more, we can allow you a special discount of 10 on the prices quoted.

Help! Water! Water!

It's the number one contaminant of groundwater, drinking water, rain water.

Finally, nearly 30 of all water on Earth is ground water.

These regular quantities are just written non bolded, while the vectors are bolded.

This is when you care about directions ... ... so you're dealing with vector quantities.

And now I can solve this by saying, look, I have two quantities.

We can't just do it into two of these now because now my ratio has three actual quantities.

Give me water, water...

Water! Someone, bring water!

What a waste of water!