What is the proper way to add vectors and what does the modulus notation mean?

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In summary, the proper way to add vectors is to use the parallelogram method, where the two vectors are drawn as adjacent sides of a parallelogram and the diagonal represents the sum of the two vectors. Modulus notation, also known as magnitude notation, is a way to represent the length or size of a vector using absolute value symbols. It is denoted by ||v|| and is equal to the square root of the sum of the squares of the individual components of the vector. This notation is useful in calculating the magnitude of a vector and determining the direction of a vector.
  • #1
synkk
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2lkpq2e.png


Could anyone explain to me what all these notations are for the vectors? I've never used vectors before and all I know is that they show direction and magnitude, but don't know the actual notation. I'm assuming OA is the vector of O to A but what is it when they put the modulus around the vector?

Any links to vectors would be great, thanks.
 
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  • #2
synkk said:
I'm assuming OA is the vector of O to A but what is it when they put the modulus around the vector?
That indicates the magnitude of the vector.
Any links to vectors would be great, thanks.
Basic Vector Operations
 
  • #3
Doc Al said:
That indicates the magnitude of the vector.

Basic Vector Operations

I see, for the magnitude you just use Pythagoras to find it? Could you not use the distance between two points?
 
  • #4
synkk said:
I see, for the magnitude you just use Pythagoras to find it?
Yes.
Could you not use the distance between two points?
That amounts to the same thing.
 
  • #5
synkk said:
I see, for the magnitude you just use Pythagoras to find it? Could you not use the distance between two points?
The formula for finding the magnitude is :

[tex]|a|=\sqrt{a_{1}^{2}+a_{2}^{2}}[/tex]
 
  • #6
hint: the absolute value of a complex number, just like any number, is its distance from zero...
 
  • #7
mtayab1994 said:
The formula for finding the magnitude is :

[tex]|a|=\sqrt{a_{1}^{2}+a_{2}^{2}}[/tex]

I'm not sure what A is.

Okay for this sketch:

1zvxrn7.png


Vector OB is 2(34)^1/2
Vector OA is 13

Now I'm reading about vectors online and it's saying that you can get to point A from OB, then to A. Now the distance from B to A is root 5, so OB to B-A should be the same as OA? Well If I add root 5 and 2(34)^1/2 it is not 13. Could anyone clear this up thanks.
 
  • #8
Basic calculation
Use a graph paper and draw the vectors to scale.
From this drawing you can find the magnitude of vector AB

Later you will be able to use vector algebra to calculate the magnitude and direction.
http://emweb.unl.edu/math/mathweb/vectors/vectors.html
 
Last edited:
  • #9
synkk said:
Now I'm reading about vectors online and it's saying that you can get to point A from OB, then to A. Now the distance from B to A is root 5, so OB to B-A should be the same as OA? Well If I add root 5 and 2(34)^1/2 it is not 13. Could anyone clear this up thanks.
It's true that the vector sum of [itex]\vec{OB} + \vec{BA} = \vec{OA}[/itex]. But you don't add vectors by simply adding their magnitudes. To learn how to add vectors (there are several ways) explore the link I gave you earlier and this one: Vector Addition.
 

FAQ: What is the proper way to add vectors and what does the modulus notation mean?

What are vectors?

Vectors are mathematical objects that have both magnitude (or size) and direction. They are commonly represented as arrows, with the length of the arrow representing the magnitude and the direction of the arrow indicating the direction.

How are vectors different from scalars?

Scalars only have magnitude, while vectors have both magnitude and direction. For example, temperature is a scalar quantity because it only has a numerical value, but velocity is a vector quantity because it has both a magnitude (speed) and a direction.

Why are vectors important in science?

Vectors are important in science because they are used to represent physical quantities such as force, acceleration, and displacement. They are also essential in many mathematical and scientific fields, such as physics, engineering, and computer graphics.

How do you add and subtract vectors?

To add or subtract vectors, you must first make sure they are in the same direction. Then, you can add or subtract the magnitudes of the vectors to get the magnitude of the resulting vector. The direction of the resulting vector will be the same as the direction of the original vectors.

Can vectors be negative?

Yes, vectors can be negative. The direction of a vector can be positive or negative depending on its orientation. For example, a vector pointing to the right may have a positive direction, while a vector pointing to the left may have a negative direction.

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