The Scalar Product, also known as the Dot Product, is a mathematical operation that takes two vectors and returns a scalar (single value) result.
The Dot Product is defined as:
A.B = ||A|| * ||B|| * cos(θ)
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
To calculate the Dot 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 cosine of the angle between the vectors, θ.
- The result of step 4 is the Dot Product of the two vectors.