Vectors of 3 components (3 dimensions)

In summary, the person is looking for resources on 3 dimensional vectors and expresses a preference for video instruction. They mention finding limited information on this topic in their textbook and online, and ask for recommendations on videos or other resources that provide comprehensive explanations. They also mention discovering Khan Academy as a potential resource.
  • #1
LearninDaMath
295
0
Hi, I don't think my textbook gives much information on vectors in 3 dimensions. The first chapter is on vectors, but only uses 2 and 1/2 pages to explain vectors in 3 dimensions. I have found a wealth of information on vectors in 2 dimensions (there are literally hundreds of detailed videos out there), but can't find much except for a 25 second video clip and one 3 and a half minute video clip on 3 dimensional vectors. Any good resources for vectors of 3 components that are explained step by step indepthly? Perhaps a video series?

P.S. I am somewhat biased towards video instruction. I know there is most likely a wealth of information on the internet for vectors of 3 components in print form, but I really prefer instruction in video format for some types of "abstract" concepts, at least at first.
 
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  • #3
thanks Dr. Morbis. I didn't realize KhanAcademy had vectors in 3 dimensions! Apparently there are other common terms for the this topic such as 3 space and R3.
 

Related to Vectors of 3 components (3 dimensions)

1. What are vectors of 3 components?

Vectors of 3 components, also known as 3-dimensional vectors, are mathematical objects that have both magnitude and direction in three-dimensional space. They are represented by three numbers or coordinates, usually denoted as (x, y, z), and can be used to describe the position, velocity, or acceleration of a point in space.

2. How are vectors of 3 components represented?

Vectors of 3 components can be represented in various forms, such as as a column or row matrix, a directed line segment, or a directed line with an arrow on top. They can also be represented using vector notation, such as v = (x, y, z).

3. What is the difference between position, velocity, and acceleration vectors?

A position vector represents the location of a point in space, a velocity vector represents the rate of change of position, and an acceleration vector represents the rate of change of velocity. In other words, a position vector tells you where an object is, a velocity vector tells you how fast and in what direction it is moving, and an acceleration vector tells you how the velocity is changing over time.

4. How are vectors of 3 components added and subtracted?

To add or subtract vectors of 3 components, you simply add or subtract the corresponding components. For example, to add two vectors v = (x1, y1, z1) and w = (x2, y2, z2), you would add the x-components (x1 + x2), the y-components (y1 + y2), and the z-components (z1 + z2) separately to get the resulting vector.

5. How do you find the magnitude and direction of a vector of 3 components?

The magnitude of a vector of 3 components is the length of the vector, which can be found using the Pythagorean theorem: |v| = √(x² + y² + z²). The direction of the vector can be found using trigonometric functions, such as the tangent function for the angle between the vector and the x-axis, or the dot product for the angle between two vectors.

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