Dot Product Calculator | Easy Vector Tool
Calculate dot product of 2D and 3D vectors instantly! Visualize vectors, understand the formula, and copy results easily. Enhance your linear algebra tasks with this user-friendly tool.
Vector a
Vector b
Result:
Understanding Dot Product
The dot product, also known as the scalar product, is a fundamental operation in linear algebra. It takes two vectors and returns a single number (scalar). Essentially, it tells us how much one vector "goes in the direction" of the other.
For two vectors \( \vec{a} = [a_x, a_y, a_z] \) and \( \vec{b} = [b_x, b_y, b_z] \), the dot product is calculated using the formula:
The result is a scalar value. A dot product of zero indicates that the vectors are orthogonal (perpendicular). A positive dot product suggests they generally point in the same direction, and a negative dot product suggests they point in opposite directions.
Dot product has wide applications in physics (calculating work), computer graphics (lighting calculations), and machine learning (similarity measures).
Learn more on Wikipedia.