Interactive Dot Product Calculator
Visualize and calculate the dot product of two vectors in an engaging way. Enter your vectors to explore their scalar product and 2D representation.
Enter Vectors
Input your vectors as comma-separated values, e.g., 1,2 or using bracket notation [1, 2]. For vectors with more than 2 components, only the dot product will be calculated.
Dot Product ( ):
2D Vector Visualization
Note: Visualization is limited to the first two components for vectors with dimensions higher than 2D.
Visualization available for 2D vectors only. Enter 2D vectors to see the plot.
Visualization is not supported for vectors with dimensions higher than 3D.
About Dot Product
The dot product, or scalar product, is a fundamental operation in linear algebra that takes two vectors and returns a single scalar value. It's calculated by multiplying corresponding components of the two vectors and summing these products.
For two vectors $$ \mathbf{A} = [a_1, a_2, ..., a_n] $$ and $$ \mathbf{B} = [b_1, b_2, ..., b_n] $$, the dot product is given by: $$ \mathbf{A} \cdot \mathbf{B} = \sum_{i=1}^{n} a_i b_i = a_1b_1 + a_2b_2 + ... + a_nb_n $$.
The dot product has geometric interpretations, especially in 2D and 3D spaces. It's related to the angle between the vectors and is used to determine vector orthogonality (perpendicularity). A dot product of zero indicates orthogonal vectors.
This calculator helps you quickly compute the dot product and visualize 2D vectors, making it easier to understand vector relationships and applications in various fields like physics, engineering, and computer graphics.