What is the difference between vector and scalar?

The easiest, non-technical way to think about it is like this:

- - A scalar is a quantity that has a size but no direction.

Those include temperature, speed, cost, volume, distance, etc.

One number is all there is to know about it, and there's no way you can

add more of the same stuff to it that would cancel both of them out.

- - A vector is a quantity that has a size and also has a direction.

Those include force, displacement, velocity, acceleration, etc.

It takes more than one number to completely describe one of these.

Also, if you combine two of the same vector quantity in different ways,

you can get different results, and they can even cancel each other out.

Here are some examples. Notice that in each of these examples,

every speed has a direction that goes along with it. This turns the

scalar speed into a vector velocity.

If you're walking inside a bus, and the bus is driving along the road,

then your velocity along the road is the sum of your walking velocity

inside the bus plus the velocity of the bus along the road.

- - If you're walking north up the middle of the bus at 2 miles per hour

and the bus is driving north along the road at 20 miles per hour, then

your velocity along the road is 22 miles per hour north.

- - If you're walking south towards the back of the bus at 2 miles per hour

and the bus is driving north along the road at 5 miles per hour, then your

velocity along the road is 3 miles per hour north.

- - If you're walking south towards the back of the bus at 2 miles per hour

and the bus is just barely rolling north along the road at 2 miles per hour,

then your velocity along the road is zero.

- - If you're in a big railroad flat-car that's rolling north along the track

at 2 miles per hour, and you walk across the flat-car towards the east

at 2 miles per hour, then your velocity along the ground is 2.818 miles

per hour toward the northeast.