Understanding Vector Notation: The Role of i, j, and k as Standard Unit Vectors

In summary: But thats just me.Ive heard one professor refer ## \hat i, \hat j, \hat k ## notion as "index notation". But thats just me.
  • #1
J-dizzal
394
6
Could anyone clarify what is the name of the i,j,k notation for vectors if there even is one?
 
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  • #2
I'm not sure what you're really asking, but the letters I, j ,k, l, m, and n are commonly used in all mathematical notation to represent integer values. It is just a convention that is attributed to Leonhard Euler.
 
  • #3
anorlunda said:
I'm not sure what you're really asking, but the letters I, j ,k, l, m, and n are commonly used in all mathematical notation to represent integer values. It is just a convention that is attributed to Leonhard Euler.

For example, if you were asked to put the components of a vector from ℝ3 in terms of the unit vectors i, j, and k what is that notation called? My professor calls it "i,j,k notation" I am wondering if there is a formal or standard name.
 
  • #4
Not that I know.
 
  • #5
Afaik, 'i' is just a simple shorthand notation symbolising an 'integer'.
If you need more than one integer to write some algorithm it's just a bit more 'understandable' to use j.k.l etc for the additional integers.
You could use i1, i2,i3 instead as symbols representing the same quantity, but that just makes thing more difficult to comprehend (imo).
 
  • #6
rootone said:
Afaik, 'i' is just a simple shorthand notation symbolising an 'integer'.
If you need more than one integer to write some algorithm it's just a bit more 'understandable' to use j.k.l etc for the additional integers.
You could use i1, i2,i3 instead as symbols representing the same quantity, but that just makes thing more difficult to comprehend (imo).

yea i agree. But there seems to be some agreement that standard unit vectors i, j, and k correspond respectively to the x, y, and z axes. Because they are standard unit vectors i thought there would be an accepted name to describe a vector in i,j,k notation rather than just say i,j,k notation.

Ive heard one professor refer ## \hat i, \hat j, \hat k ## notion as "index notation".
 
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What is vector notation?

Vector notation is a mathematical system used to represent vectors, which are quantities that have both magnitude and direction. It is commonly used in physics, engineering, and other scientific fields.

How is a vector represented in vector notation?

A vector is typically represented by an arrow over a letter, such as →A. The length of the arrow represents the magnitude of the vector, and the direction of the arrow represents the direction of the vector.

What are the components of a vector?

A vector has two main components: magnitude and direction. The magnitude is the size or length of the vector, while the direction is the angle at which the vector is pointing.

What are the different types of vector notation?

There are several types of vector notation, including standard notation (using letters with arrows), unit vector notation (using a unit vector i, j, or k), and component notation (using numerical values for the vector's components).

How is vector notation used in calculations?

In vector notation, vectors are added, subtracted, and multiplied using specific rules and formulas. These calculations are important in many scientific fields, including physics and engineering, to determine the outcome of various physical processes.

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