# Left-Handed Coordinate System: Unit Vectors i,j,k

• qwerty11
In summary, The Cartesian coordinate system is a right-handed system that is commonly but not universally defined by a left-handed coordinate system. This can be confusing and lead to misunderstandings with those who work with other coordinate systems such as north-east-up.
qwerty11
A friend asked me this question today. It kinda threw me for a loop. The cartesian coordinates system is a left handed coordinate system right, so therefroe they are defined by a left handed coordinate syste correct?

The Cartesian coordinate system is a right-handed system.

Does your "friend" live in that square of glass in your bathroom and have an uncanny knack for mimickry?

Mark44 said:
The Cartesian coordinate system is a right-handed system.
Not necessarily. That is an extremely common, but not universal, convention.

HallsofIvy said:
Or he/she is a geologist, or a radar technician, or a GPS specialist, or someone else who (danged annoyingly!) works with north-east-up coordinates.

aikismos

## 1. What is a left-handed coordinate system?

A left-handed coordinate system is a mathematical system used to represent points, lines, and shapes in three-dimensional space. It is based on the concept of three perpendicular axes, each representing a different dimension (x, y, and z). In a left-handed coordinate system, the x-axis points to the left, the y-axis points down, and the z-axis points away from the viewer.

## 2. What are unit vectors i, j, and k in a left-handed coordinate system?

In a left-handed coordinate system, unit vectors i, j, and k are used to represent the directions of the x, y, and z axes, respectively. These unit vectors have a magnitude of 1 and are used to define the direction and orientation of points, lines, and shapes in three-dimensional space.

## 3. How are unit vectors i, j, and k related to each other in a left-handed coordinate system?

In a left-handed coordinate system, unit vectors i, j, and k are perpendicular to each other. The i-axis is perpendicular to both the j-axis and k-axis, the j-axis is perpendicular to both the i-axis and k-axis, and the k-axis is perpendicular to both the i-axis and j-axis.

## 4. How do you use unit vectors i, j, and k to represent a point in a left-handed coordinate system?

To represent a point in a left-handed coordinate system, you would use a combination of the three unit vectors. The coordinates of the point would be expressed as a linear combination of the unit vectors, with each vector representing a different direction. For example, the point (3, 2, 4) would be represented as 3i + 2j + 4k.

## 5. What is the significance of using a left-handed coordinate system?

The use of a left-handed coordinate system is a convention that allows for consistency and standardization in mathematical calculations and visual representations in three-dimensional space. It is also important in fields such as physics and engineering, where the direction and orientation of objects and their movements are crucial for analysis and problem-solving.

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