Dot Product Calculator

Dot Product Calculator

Compute the scalar dot product of two 3D vectors.

Last updated: June 2026 | By Patchworkr Team

Vector Dot Product

Vector A

Vector B

Dot Product

Enter all six vector components as real numbers.

What is the Dot Product?

The dot product multiplies matching components and adds them together.

A dot B = a1*b1 + a2*b2 + a3*b3

It is a scalar value and is zero when the vectors are perpendicular.

How to Use

1. Enter the three components of vector A.

2. Enter the three components of vector B.

3. Read the live scalar result and the component products.

Worked Example

For A = (2, 3, 1) and B = (4, 1, 2):

A dot B = 2*4 + 3*1 + 1*2 = 8 + 3 + 2 = 13

The calculator should show 13.

FAQ

Can the result be negative?

Yes. A negative dot product means the vectors point more than 90 degrees apart.

When is it zero?

When the vectors are perpendicular, or one vector is zero.

Is it commutative?

Yes. A dot B equals B dot A.

Does the formula change in higher dimensions?

No. Multiply matching components and add them all.

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