Quickly calculate the scalar product (also known as the dot product) of two 3D vectors. Understand how to find the projection of one vector onto another and determine the angle between them. Essential for physics, engineering, and computer graphics.
Formula:
For two 3D vectors A = (Ax, Ay, Az) and B = (Bx, By, Bz), the scalar product (dot product) is given by:
A ⋅ B = AxBx + AyBy + AzBz
Where:
- Ax, Ay, Az are the components of Vector A.
- Bx, By, Bz are the components of Vector B.
The magnitude of a vector V = (Vx, Vy, Vz) is |V| = √(Vx2 + Vy2 + Vz2).
The angle θ between vectors A and B is found using cos(θ) = (A ⋅ B) / (|A| |B|).