Dot Product Calculator

Calculate the dot product (scalar product) of two vectors and related properties.

Vector Dimensions

Vector A

a1

a2

a3

A = (1, 2, 3)

Vector B

b1

b2

b3

B = (4, 5, 6)

Calculation Steps

A . B = sum of (ai * bi)

= (1 * 4) + (2 * 5) + (3 * 6)

= 4 + 10 + 18

= 32

Dot Product A . B

32.000000

|A|

3.7417

|B|

8.7750

Angle

12.93 deg

cos(theta)

0.974632

Vector Relationships

Orthogonal?No

Parallel?No

Projection of A onto B

Scalar projection

3.646738

Vector projection

(1.6623, 2.0779, 2.4935)

Properties

A . B = B . A (commutative)
A . (B + C) = A . B + A . C (distributive)
A . A = |A|^2
A . B = |A||B|cos(theta)