Vector Angle Calculator
Calculate the angle between two vectors, projections, and related properties.
Vector Input
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
Formula
cos(θ) = (v₁ · v₂) / (|v₁| × |v₂|)
cos(θ) = 32.0000 / (3.7417 × 8.7750) = 0.974632