🔀 Dot Product Calculator
Calculate the dot product of two vectors, along with their magnitudes and the angle between them. Leave the z components at 0 for 2D vectors.
What the dot product tells you
The dot product (also called the scalar product) combines two vectors into a single number that reflects how much they point in the same direction. A positive dot product means the vectors point somewhat the same way, a negative one means they point somewhat opposite, and zero means they are perpendicular.
The formula used
For vectors A = (ax, ay, az) and B = (bx, by, bz), the dot product is A · B = ax·bx + ay·by + az·bz. The angle between the vectors is then found with cos(θ) = (A · B) / (|A|·|B|), where |A| and |B| are the vector magnitudes.
For 2D vectors, simply leave the Z components set to 0. This tool is intended for general math, physics, and engineering learning purposes.