Wrapping my mind around vectors?

  • Context: Undergrad 
  • Thread starter Thread starter lrl4565
  • Start date Start date
  • Tags Tags
    Mind Vectors
Click For Summary

Discussion Overview

The discussion revolves around understanding the nature of vectors and scalars, exploring their definitions, properties, and applications. Participants raise questions about the coexistence of magnitude and direction in vectors, the implications of negative scalars, and the significance of vectors in various contexts, such as velocity and displacement.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants define scalars as quantities with magnitude only, while vectors have both magnitude and direction.
  • There is confusion about how magnitude and direction coexist in vectors, with questions about what a vector is doing and how it is represented.
  • Participants inquire whether scalars can be negative, with examples like temperature and charge density being discussed.
  • One participant suggests that vectors are useful for describing quantities where location matters, such as velocity.
  • Another participant provides an example of an airplane's velocity to illustrate how magnitude and direction are combined in vectors.
  • There is a discussion about the relationship between vectors and coordinate systems, with questions about whether the Cartesian coordinate system consists of scalars.
  • Some participants express a desire to clarify the differences between vectors and scalars, particularly in terms of their applications in physics.

Areas of Agreement / Disagreement

Participants generally agree on the definitions of scalars and vectors, but there are multiple competing views regarding the implications of negative scalars and the conceptual understanding of vectors. The discussion remains unresolved on several points, particularly regarding the nature of magnitude in scalars and the role of vectors in various contexts.

Contextual Notes

There are limitations in the discussion regarding the assumptions made about the definitions of scalars and vectors, as well as the mathematical relationships involved in their applications. Some participants express uncertainty about the implications of negative values in scalars and how they relate to vector quantities.

lrl4565
Messages
19
Reaction score
0
So, I'm assuming that scalars are what I'm used to working with in math. You add, subtract, multiply, etc.; they follow the rules I know. 1 + 1 = 2.

Scalar = Magnitude

Vector = Magnitude and Direction

Now, how do magnitude and direction coexist? Right now I'm just seeing some scalar volume cube being moved in a certain direction. What is the vector DOING? Can you provide me with a solid example of vectors at work?A vector measures displacement... the distance from start to ending point. So how can they have arrows indicating their direction? They must be finite, but they look like rays.

It doesn't matter where you put a vector on cartesian or polar coordinates... but then we're supposed to calculate the vector using scalar components. If Vector C is 5 long, how can the square root of (really big number A squared) + (really big number B squared) equal really small number 5?

In addition, what ARE vectors? I mean, why are we taking the displacement instead of the distance, and adding some angle?
 
Last edited:
Physics news on Phys.org
Can scalars be negative?

Or are they the absolute value?

Distance (scalar) is always positive, but temperature (scalar) is more confusing... would -30 degrees just be... 30 degrees?
 


Yes they can be negative. Think of charge density for instance.
 


Alright... vectors deal with things where location matters.

Can you give me an example of how a vector would be useful? How magnitude and direction can coexist?
 


They can be.For Example Work Can be Negative.
 


lrl4565 said:
Alright... vectors deal with things where location matters.

Can you give me an example of how a vector would be useful? How magnitude and direction can coexist?

Velocity.

Something that is moving, is moving at a certain speed, in a certain direction.

If an airplane is flying in the air, it has a velocity, say, 600 km/h in a direction north-east.

That's a vector: the magnitude is 600 km/h and the direction is north-east.
 
BTW, I merged this with your other thread, as I think both questions are related.
 
Scalar = magnitude. So can magnitude be negative?
 
lrl4565 said:
Scalar = magnitude. So can magnitude be negative?

No, scalar is not ALWAYS a magnitude. A magnitude is a scalar, however.
 
  • #10
So, my main goal in asking these questions is to determine WHAT a vector is, why they exist, and how they differ from scalars.

What I have so far:

The purpose of vectors is to make it simpler to deal with "things" that have both a distance and a location... so velocity HAS to have a location? Wow, it really is not at all like speed.

OK, why do I want to know it's location?

Let's see... we put the vectors onto coordinate systems, like the cartesian coordinates. And we use scalars to plot things on the cartesian coordinates, so we break down the vector into components in order to plot it on the cartesian coordinate system.

Does this mean that the cartesian coordinate system is made up of scalars?
 
  • #11
So, magnitude is the absolute value of the displacement?

Err, wait, scalar = distance
 
  • #13
lrl4565 said:
So, my main goal in asking these questions is to determine WHAT a vector is, why they exist, and how they differ from scalars.

What I have so far:

The purpose of vectors is to make it simpler to deal with "things" that have both a distance and a location... so velocity HAS to have a location? Wow, it really is not at all like speed.

OK, why do I want to know it's location?

Let's see... we put the vectors onto coordinate systems, like the cartesian coordinates. And we use scalars to plot things on the cartesian coordinates, so we break down the vector into components in order to plot it on the cartesian coordinate system.

Does this mean that the cartesian coordinate system is made up of scalars?

Velocity has a magnitude and direction. This is important because when two vector quantities interact with each other the direction they move is important. It is simpler than you are making it. Let's say that you have a plane flying at x mph and there is a wind directly behind it blowing at y mph. The wind will add to the planes speed. If the wind is blowing directly toward the plane it will subtract from its speed. If the wind is blowing at an angle toward the plane it will push the plane in the direction of the angle. The direction involved in vectors is just an easy way of taking all of this into account when you are solving this problem of how the wind and plane will interact.
 

Similar threads

High School Is velocity ever a scalar quantity?
  • · Replies 48 ·
2
Replies
48
Views
7K
Undergrad Why is momentum considered a vector and kinetic energy a scalar?
  • · Replies 15 ·
Replies
15
Views
4K
High School Misleading Textbook Equation for vf^2=vi^2 + 2ad
  • · Replies 3 ·
Replies
3
Views
3K
High School What does the scalar product of two displacements represent?
  • · Replies 8 ·
Replies
8
Views
1K
Undergrad Measuring Vectors: Defining Direction and Magnitude
  • · Replies 20 ·
Replies
20
Views
3K
Undergrad Controversy about the nature of finite angular displacement
  • · Replies 15 ·
Replies
15
Views
3K
Undergrad Off center torque applied to a rotating body
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Determining Whether Solution is Vector vs Scalar?
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad Pendulum Tension Force -- How to calculate the full vector?
  • · Replies 39 ·
2
Replies
39
Views
6K
Undergrad Work: Dot Product and Integral?
  • · Replies 7 ·
Replies
7
Views
3K