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3D Vector Scalar Product Calculator

The 3D Vector Scalar Product calculator helps you find the dot product (scalar product) of two three-dimensional vectors. It’s useful in physics, engineering, and computer graphics to measure how much two vectors align or to find the angle between them. Just input the components of both vectors and get the scalar result instantly.

3D Vector Scalar Product Calculator Calculator

Input Fields
If enabled, the result will update automatically when you change any value.

Dot Product Formula for 3D Vectors

Formula
$$\vec{A} \cdot \vec{B} = A_x B_x + A_y B_y + A_z B_z$$

Where:

  • $$\vec{A} = (A_x, A_y, A_z)$$
  • $$\vec{B} = (B_x, B_y, B_z)$$
  • The result is a scalar, not a vector.

This formula multiplies corresponding components of the vectors and sums them up.

The scalar (dot) product is a fundamental operation in vector mathematics. It’s often used to determine the angle between two vectors, to check orthogonality (if the result is 0), or to project one vector onto another. For example, in 3D graphics, it’s essential for lighting calculations and camera orientation. Simply input the x, y, and z components of both vectors, and the calculator will return the scalar result.

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