# How do you represent vectors in a 3D space?

• phy-79
In summary, a vector in 3D space is a quantity with both magnitude and direction, represented by an arrow from the origin to a specific point. Vectors are represented mathematically using three components and can be added/subtracted by combining their components. Position vectors locate a point, while direction vectors only show direction. Vectors can also be multiplied using dot or cross products.
phy-79
I have problems in understanding what RECIPROCAL VECTORS are...
I know the formulas regarding it but don't know their geometric meaning is...
How do you represent them in a 3D spcace ?

phy-79 said:
I have problems in understanding what RECIPROCAL VECTORS are...
I know the formulas regarding it but don't know their geometric meaning is...
How do you represent them in a 3D spcace ?

## 1. What is a vector in 3D space?

A vector in 3D space is a quantity that has both magnitude and direction. It is represented by an arrow that starts at the origin and extends to a specific point in 3D space.

## 2. How are vectors represented mathematically in 3D space?

Vectors in 3D space are typically represented using three numbers, known as components, which indicate the magnitude of the vector in the x, y, and z directions. These components can be represented using coordinates or as column or row matrices.

## 3. What is the difference between a position vector and a direction vector?

A position vector is used to locate a point in 3D space relative to the origin. It has both magnitude and direction. A direction vector, on the other hand, only indicates the direction in which a vector is pointing and has a magnitude of 1.

## 4. How are vectors added and subtracted in 3D space?

To add or subtract vectors in 3D space, we simply add or subtract their corresponding components. For example, to add two vectors, we add their x, y, and z components separately. This is known as vector addition/subtraction.

## 5. Can vectors be multiplied in 3D space?

Yes, vectors in 3D space can be multiplied, but not in the traditional sense of multiplication. The two types of vector multiplication in 3D space are dot product and cross product. Dot product results in a scalar quantity, while cross product results in a vector quantity.

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