2D Vector Dot Product Calculator with Formula & Interactive Graph

Calculator

Interactive Calculator

Move the sliders to change vectors A and B. The animated graph updates instantly with dot product and angle.

Vector A

Vector B

A B

Calculation

Formula

The inner product or scalar product of two vectors can be defined as:
A * B = |A| * |B| * Cos(theta)
Where: |A| and |B| represents the magnitudes of vectors A and B,
     (theta) is the angle between vectors A and B.

Lets consider the two vector A and B for dot or scalar product.

The dot product is a form of multiplication that involves two vectors having the same number of components. To determine the dot product of two vectors, we always multiply like components, and find their sum.

Let us consider vector A as (2,3) and vector B as (4,6).

The A*B = a1* b1 + a2* b2

=(2 × 4) + (3 × 6)

= 8 + 18

= 26

Frequently Asked Questions

What is the dot product of two vectors?

The dot product is obtained by multiplying corresponding components and adding them.

What happens when dot product is zero?

The vectors are perpendicular.

Can dot product be negative?

Yes. Negative dot product means vectors point in opposite directions.