# Angle Between Diagonal of Cube Calculator

A cube is a three dimensional object with six faces and three of them meeting at each vertex. The angle formed between one of the diagonal and its edge can be calculated with this calculator. Select the diagonals for which you want to find the angle and enter the vectors of the diagonal.

A cube is a three dimensional object with six faces and three of them meeting at each vertex. The angle formed between one of the diagonal and its edge can be calculated with this calculator. Select the diagonals for which you want to find the angle and enter the vectors of the diagonal.

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### Example

**If the vectors of the diagonal OF and AG are (0,0,0), (1,2,3), (1,2,1) and (1,1,1).**

#### Step : 1

Vector OF = (1,2,3) - (0,0,0) = (1,2,3)

Vector AG = (1,1,1) - (1,2,1) = (0,-1,0)

#### Step : 2

OF. AG = |OF| - |AG| cos θ

(1,2,3) . (0,-1,0) = [√(1^2+2^2+3^2) . √((-1)^2) ] cos θ

(0 + (-2)+ 0 = [√(14) . √1]cos θ

-2 = √14 cos θ

cos θ = -2 / 3.741

cos θ = -0.5346

#### Step : 3

θ = cos ^{-1}-0.5346

θ = 122.316 ° (or) 2.1347 rad