Infinite number of perpendicular vectors?

• Maybe_Memorie
In summary, we find unit vectors A' and B' parallel to vectors A and B respectively. Then, we construct all unit vectors C orthogonal to A' and B', and finally, we can find a unit vector D such that C.D = 0. This can be done since there is an infinite number of vectors that meet this criteria.
Maybe_Memorie

Homework Statement

Let A and B be vectors
A = (2,-1,3) B = (1,4,1)
a) Find unit vectors A' and B' parallel to A and B respectively. Done.

b) Construct all the unit vectors C, orthogonal to A' and B'. Done.

c) Construct a unit vector, D, such that
C.D = 0.

Isn't there an infinite number of vectors that meet this criteria?

Maybe_Memorie said:
b) Construct all the unit vectors C, orthogonal to A' and B'. Done.

c) Construct a unit vector, D, such that
C.D = 0.

Isn't there an infinite number of vectors that meet this criteria?

Well I think they just want you to find one, which you can do since you did part b already.

1. What is an infinite number of perpendicular vectors?

An infinite number of perpendicular vectors refers to a set of vectors that are all perpendicular to each other, meaning they form right angles when placed together. This set can continue infinitely in any direction.

2. How is an infinite number of perpendicular vectors used in mathematics?

Infinite perpendicular vectors are used in various mathematical concepts such as vector calculus, linear algebra, and geometry. They can be used to solve problems involving direction, displacement, and magnitude.

3. Can an infinite number of perpendicular vectors exist in three-dimensional space?

Yes, an infinite number of perpendicular vectors can exist in three-dimensional space. This is because three-dimensional space allows for multiple planes and dimensions, making it possible for an infinite number of perpendicular vectors to exist.

4. Are there any real-life applications of infinite number of perpendicular vectors?

Yes, there are many real-life applications of infinite number of perpendicular vectors. For example, they are used in engineering and architecture for designing structures, in physics for calculating forces and motion, and in computer graphics for creating three-dimensional images.

5. How can one determine if two vectors are perpendicular to each other?

To determine if two vectors are perpendicular, you can use the dot product. If the dot product of two vectors is zero, then they are perpendicular. Another method is to calculate the angle between the two vectors; if the angle is 90 degrees, then the vectors are perpendicular.

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