- The Vector Product, also known as the Cross Product, is a mathematical operation that takes two vectors and returns another vector as the result.
- Unlike the Scalar Product (or Dot Product), the Cross Product gives information about the direction of the result vector, as well as its magnitude.
The Cross Product is defined as:
A x B = ||A|| * ||B|| * sin(θ) * n
Where:
A and B are the two vectors
||A|| and ||B|| represent the magnitude (length) of the vectors A and B
θ is the angle between the two vectors A and B
n is a unit vector that defines the direction of the result vector
To calculate the Cross Product step by step:
- Calculate the magnitudes of the two vectors: ||A|| and ||B||.
- Calculate the angle between the two vectors, θ.
- Multiply the magnitudes of the two vectors: ||A|| * ||B||.
- Multiply the result of step 3 by the sine of the angle between the vectors, sin(θ).
- Determine the direction of the result vector using a right-hand rule.
- Multiply the result of step 4 by the unit vector in the direction determined in step 5, n.
- The result of step 6 is the Cross Product of the two vectors, represented as a vector.