Dot Product Calculator
The dot product (also known as the scalar product) is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors) and returns a single number.
For two 3-dimensional vectors:
A = [Ax, Ay, Az]
B = [Bx, By, Bz]
The dot product is calculated as:
A · B = (Ax × Bx) + (Ay × By) + (Az × Bz)
How to Use:
- Enter the x, y, and z components for Vector A.
- Enter the x, y, and z components for Vector B.
- Click “Calculate Dot Product”.
The result is a scalar value. The dot product is useful in determining the angle between two vectors, projecting one vector onto another, and in various physics and engineering applications.
This calculator is currently set for 3D vectors. The general formula for n-dimensional vectors A = [A1, …, An] and B = [B1, …, Bn] is: A · B = Σ (Ai × Bi) for i=1 to n.
Calculate the scalar product of two 3D vectors.
Dot Product (A · B)
The dot product is a scalar quantity.
- If A · B > 0, the angle between the vectors is acute (less than 90°).
- If A · B = 0, the vectors are orthogonal (perpendicular, 90°).
- If A · B < 0, the angle between the vectors is obtuse (greater than 90°).