Vector Angle Calculator

Calculate the angle between two vectors, projections, and related properties.

Vector Input

Dimension

Vector 1

Vector 2

|v₁| =

3.7417

|v₂| =

8.7750

Angle Between Vectors

12.9332°

0.225726 radians

Products

Dot Product (v₁ · v₂)

32.0000

Cross Product (v₁ × v₂)

(-3.0000, 6.0000, -3.0000)

Projection of v₁ onto v₂

Scalar Projection

3.646738

Vector Projection

(1.6623, 2.0779, 2.4935)

Areas

Parallelogram

7.3485

Triangle

3.6742

cos(θ) = (v₁ · v₂) / (|v₁| × |v₂|)

cos(θ) = 32.0000 / (3.7417 × 8.7750) = 0.974632