2D Vector Scalar Product Calculator
The 2D Vector Scalar Product Calculator helps you compute the scalar (dot) product of two 2D vectors. This tool is useful for students, engineers, and anyone working with vector mathematics. It takes the x and y components of each vector and returns a single number representing their scalar product, which can indicate the angle relationship between them.
Calculate the Dot Product of Two 2D Vectors
Dot Product Formula for 2D Vectors
Where:
- $$A_x, A_y$$ — components of vector A
- \(B_x, B_y\) — components of vector B
This formula calculates the scalar product by multiplying the corresponding components of two vectors and summing the results.
The scalar (dot) product of two 2D vectors measures how much one vector extends in the direction of another. It is commonly used in physics, computer graphics, and engineering to determine angles between vectors, check for orthogonality (dot product = 0), or project one vector onto another.
For example, if \(\vec{A} = (2, 3)\) and \(\vec{B} = (4, -1)\), the dot product is \(2 \cdot 4 + 3 \cdot (-1)\) = 8 – 3 = 5. A positive result indicates an acute angle between vectors, zero means they are perpendicular, and negative indicates an obtuse angle.