A vector is a mathematical quantity that has both magnitude (size) and direction. It is often represented by an arrow with its length representing its magnitude and its direction indicating the direction of the vector.
Vectors are typically written using bold letters, such as v, or with an arrow on top, such as →v. They can also be written as a column matrix with the components listed vertically, such as [vx, vy, vz].
A cross product is a mathematical operation that produces a vector which is perpendicular to both of the vectors being multiplied. It is denoted by the symbol × and is only defined in three-dimensional space.
The cross product of two vectors a and b can be calculated using the following formula: a × b = [aybz - azby, azbx - axbz, axby - aybx]. This will result in a vector that is perpendicular to both a and b.
Vectors and cross products have various applications in science and engineering. They are commonly used in physics to represent forces and velocities, in engineering for structural analysis and mechanics, and in computer graphics for 3D transformations and animations. They are also used in many other fields, such as navigation, robotics, and even biology.