I know v(t) is vector value and |v(t)| is a "scalar"

>>8396742
A scalar has one property, magnitude. I am moving at 100 miles per hours, i could be in a rocket headed out of earth's orbit, in a car on the freeway, in a submarine going underwater, etc. Inherently in a scalar definition there is no direction defined.

A vector on the other hand has a magnitude and specific direction.

In math terms the absolute value is useful for things moving in one dimension, forward or backwards. A magnitude of 6 doesnt say away from the starting point or towards it, but a vector does define what direction is being traveled.

>>8396742
v (t) has an implied direction. Usually this is denoted by ijk or xyz with hats for vector and dots for scalar but often omitted.

Also, a scalar has no units.

>>8396747
>>8396745
so how exactly does a car traveling with a velocity of 8m/s differ from a car traveling with a speed of 6m/s?

Finance/Econ major taking Calc III and just curious

Your example of v(t) is still a scalar. A vector is denoted in component notation (a,b), basis notation ai + bj, or column notation.

>>8396747
>Also, a scalar has no units.
That's false.

>>8396747
>>8396745
to elaborate on >>8396752
v(t)= 3ti+5k
where i is the x component and k is the z component

>>8396752
(0,0) -> (5,5) in one second is a vector.
sqrt(50) is a scalar.

The difference is that, with the vector, you'll be given things like "20 degrees north of the azimuth" and, with the speed, you'll be given a ten year old nagging you saying "How do you know how far a car has gone in five seconds if it goes ten meters per second?"

>>8396759
also z is defined by altitude and x is forward motion

>>8396765
>>8396742
To put in perspective of a problem,
a car experiences a force describe by vector A for five second, then described by vector B for ten seconds. Vector A is 100 N at 20 degrees north of east, and vector B is 100 N at 20 degrees south of west. What's the car's current velocity, in what direction, for a car of mass 1,000kg, 5,000kg, and 10,000kg?

>>8396765
>>8396775
so the vector is only the inputing force while the speed is the "output"?


>tfw do fine in theortical math but a bainlet with this applied stuff

>>8396786
Speed is how fast you're moving relative to something else.

A vector is anything with a magnitude and direction. Whether that's a force of X newtons directly north, a speed of Y m/s heading directly east.

I'm really struggling to understand where your comprehension is breaking off. Maybe you're over-complicating all of this?

>>8396794
>A vector is anything with a magnitude and direction
hate this meme

>>8396796
Did you throw a tantrum when your grade-school teachers said "You can't subtract a bigger number from a smaller number because zero is the smallest number"?

It's incorrect, but correct teaching.

>>8396794
>I'm really struggling to understand where your comprehension is breaking off. Maybe you're over-complicating all of this?
frug it, Im not an engieneering or physics major and I dont need to define it for calc III

Ill just stay a physics brainlet

File: Capture.png (47KB, 490x215px) Image search: [Google]

47KB, 490x215px

>>8396802
I mean, for one last ditch effort, just running through a chapter on it and solving some of the problems might give you an intuitive understanding, which can lead you to a practical, defined understanding.

>>8396799
Honestly, my problem with it is saying that is something with magnitude.

A vector is something with direction, that's it, you don't need to say it has a magnitude, because magnitude is optional.
In my language they even added another requirement which is pretty much the equivalent of direction, and just needlessly confused students, because they had to recite that damned definition with the slight variation.

So yes, I did, and developed a hatred for it.

>>8396799
>It's incorrect, but correct teaching.

brainlet cop-out response

>>8396742
https://www.youtube.com/watch?v=fNk_zzaMoSs

>>8396759
In your example, if I dump the t, so I can set a more clear example, I see you moving with a velocity of 3 in the x direction,
And you also have a velocity of 5 in the z direction, which is constant.

That's your vector, it tells me exactly how you are moving in different directions.

The magnitude |v(t)| tells me the velocity you're moving away from me in total.

Think of it terms of distance, if I say to get to some street you need to move 3 blocks in the x direction and 5 blocks in the z direction.
That's once again, another vector example, it tells you exactly how things behave in each direction.

The magnitude here would tell you how far you are from the point you started.

>>8396742
>If v(t) = 3t+5 then v(1) = 8 m/s and |v(t)| = ~6 m/s
American education.

>>8396759
In that case, your v(1) is not 8 m/s. It's 3 m/s in the x direction and 5 m/s in the z direction. You can't just add different velocity components.

>>8396742
>>8396752


Uh lets try it this way. In the most general terms a scalar is saying, as i described before, moving at 100 mph. Could be up down, in circles, left, right etc.

But a vector would say i am moving 100mph at an angle of 30 degrees west of north, starting exactly at coordinate (231.2, 1232.1)Thus a vector tells you how fast and whether it is up, down, left, right.

Scalars have only on quality, magnitude. Vectors have two qualities, magnitude and direction.

A scalar is just a number or a value
So like the plane is moving at 500km/h. A vector is a scalar with direction so the plane is moving 500km/h South West.

The vector will have components relative to an axis so in math these are i j k, in physics this could be velocity in thr x direction and velocity in the y direction and a scalar will not since it's just a value, with no orientation (don't assume its gender).

>>8396742
Is |v(t)| supposed to be |v(1)|? Cuz then its
[math] |v(1)| = \sqrt{3^2 + 5^2} [/math]
Which is around 5.83 and then u round to get 6

>>8396815
>A vector is something with direction, that's it
get a load of this guy
if you're going to be autistic, you can't even refine your notion of direction (or magnitude) unless you're talking about inner product spaces

>>8397098
3t + 5 = v(t) is a single component vector, , so v(1) = 8 and ||v(1)|| = sqrt((3*(1)+5)^2) = 8

>>8397197
So what's the problem?
We can naturally consider direction with the basis only, and can stick a system of coordinates there with only that.

Everything else is just more structure, but is not required for something to be a vector.

>>8397419
just pointing out that you get mad over the easy to understand notion of "something with a direction and magnitude" and want to replace it with "something that has a direction" which is obviously a bunch of vague garbage, and for that I pointed out that you don't even have a notion of direction unless you're in an inner product space

and no, having a basis does not suffice

>>8397459
Yes it does suffice with that.

If i say ai + bj, it means a in the DIRECTION of i and b in the direction of j