Why do we use ijk for vectors?

The use of i, j, and k for vectors in three-dimensional space comes from the convention of expressing vector components along the three axes of a Cartesian coordinate system.

Vector Components: A vector in 3D space can be represented as a combination of its components along the x, y, and z axes. These components are scalar quantities that indicate how much of the vector lies along each axis.

Unit Vectors: The symbols i, j, and k represent unit vectors along the x, y, and z axes, respectively. A unit vector is a vector with a magnitude of 1, and it is used to specify direction.

i represents the unit vector along the x-axis.
j represents the unit vector along the y-axis.
k represents the unit vector along the z-axis.
Representation of Vectors: A vector v in three-dimensional space can be written as a linear combination of these unit vectors:

v = xi + yj + zk
Here, x, y, and z are the scalar components of the vector along the x, y, and z axes, respectively.
The vector v is thus a combination of these components, with i, j, and k providing the directionality along each axis.
History and Standardization: The use of i, j, and k dates back to the work of mathematicians and physicists in the 19th century, especially in the context of vector analysis and three-dimensional geometry. These letters were chosen arbitrarily as they are simple and easy to distinguish. The convention became widely accepted and standardized.

In summary, i, j, and k are used for vectors because they denote the unit vectors along the x, y, and z axes in 3D space. They help break down a vector into its components along each axis, making calculations and vector operations easier.