noeinstein said:They have the same/opposite direction?
The vector cross product, also known as the vector or cross product, is a mathematical operation that takes two vectors as input and produces a third vector that is perpendicular to both of the input vectors.
The formula for calculating the vector cross product is:
a x b = |a||b| sin θ n
where a and b are the two input vectors, |a| and |b| are their magnitudes, θ is the angle between them, and n is a unit vector perpendicular to both a and b.
The vector cross product has the following properties:
- It is not commutative: a x b ≠ b x a
- It is distributive: a x (b + c) = a x b + a x c
- It follows the right-hand rule: the direction of the resulting vector is perpendicular to both a and b, and is determined by curling the fingers of your right hand from a to b
- The magnitude of the resulting vector is equal to |a||b| sin θ, where θ is the angle between a and b.
The vector cross product has many real-life applications, including:
- Calculating the torque on a rotating object
- Finding the direction of magnetic fields
- Determining the angular momentum of a spinning object
- Solving problems in fluid mechanics
- Creating 3D graphics in computer programming
The vector cross product and the dot product are two different mathematical operations involving vectors. While the vector cross product produces a third vector, the dot product produces a scalar (a number). They are related in the sense that the dot product of two perpendicular vectors is equal to 0, and the cross product of two parallel vectors is also equal to 0.