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.

Code to add this calci to your website Expand embed code Minimize embed code

Formula:

OF and AG BD and CE OF and CE GA and BD x = A⃗B⃗ . C⃗D⃗ = |AB|.|CD| cos θ θ = cos-1 * √(x) Where, θ = Angle Between Diagonal of Cube cos = Cosine x = Vector

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

english Calculators and Converters