Special Numbers in R3: a, b & c

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In summary, special numbers in R3 are numerical values with unique properties in three-dimensional space and are used in various scientific fields. A, b, and c represent the three axes in R3, and special numbers can be represented using these coordinates. They differ from regular numbers in their properties and use in solving complex equations. Examples of special numbers in R3 include imaginary, real, complex, and irrational numbers. These numbers are applied in real-world scenarios such as physics, engineering, mathematics, and computer graphics.
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MPQC
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Homework Statement



"Whats special about vectors a, b, and c with respect to R3"

a= (1,2,-3)
b= (-2,5,8)
c= (1,3,5)

Homework Equations



N/A

The Attempt at a Solution



N/A, I see nothing special about them.
 
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  • #2
Vectors can span a space, so maybe your vectors span R3. How could you check this?
 
  • #3
Although it might be a spanning set I don't think that is the special property.
 

1. What are special numbers in R3?

Special numbers in R3 are specific numerical values that have unique properties in three-dimensional space. These numbers are used in various scientific fields, including physics, mathematics, and engineering.

2. What is the significance of a, b, and c in special numbers in R3?

A, b, and c represent the three axes in three-dimensional space: x, y, and z, respectively. These letters are commonly used to denote the coordinates of a point in R3, which can be used to express special numbers.

3. How are special numbers in R3 different from regular numbers?

Special numbers in R3 have unique properties and can be represented in three-dimensional space, while regular numbers are one-dimensional and do not have these specific properties. Special numbers in R3 are also used to solve complex equations and problems in fields such as physics and engineering.

4. What are some examples of special numbers in R3?

Examples of special numbers in R3 include imaginary numbers, such as i (the square root of -1), and real numbers, such as pi (π). Other examples include complex numbers, such as 3+4i, and irrational numbers, such as the square root of 2 (√2).

5. How are special numbers in R3 used in real-world applications?

Special numbers in R3 are used in a variety of real-world applications, such as in physics to describe the motion of particles, in engineering to design structures and machines, and in mathematics to solve complex equations. They are also used in computer graphics to create three-dimensional images and animations.

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