Calculate Angle Between 2 Lines in 3D - Easy Formula

[ikeoe]

Homework Statement

Can someone help me to find angle between 2 lines in 3D? I have 2 lines from (-x, 0, -y) to (0, 0, 0) to (0, x, y). I can use CAD to get the answer. But my shop guys will need some kind of formula. The easier way please, thank all.

Homework Equations

Example: (-10, 0, -6) to (0, 0, 0) to (0, 10, 6) is 105.3 degree.

The Attempt at a Solution

 

[tiny-tim]

Welcome to PF!

Can someone help me to find angle between 2 lines in 3D? I have 2 lines from (-x, 0, -y) to (0, 0, 0) to (0, x, y). I can use CAD to get the answer. But my shop guys will need some kind of formula. The easier way please, thank all.

Hi ikeoe! Welcome to PF!

(what's CAD? )

Hint: a.b = |a| |b| cos θ,

so cos θ = a.b/√(a.a)√(b.b)

 

[Tac-Tics]

Say you have three points, A, B, C. You want to find the angle between lines AB and BC.

You can represent lines by vectors. Line AB would be the vector A - B and BC would be the line B - C. Then, to get the angle, you just need to use the dot product formula:

x * y = |x| |y| cos(theta)

Where * is the dot product, |x| is the length of the vector x, and theta is the smallest positive angle between the two vectors.

I'll leave the algebra to you.

 

[ikeoe]

Thank you, tiny-tim. CAD is Computer Aided Design mostly used from AutoDesk AutoCAD.

 

[ikeoe]

Great, thanks to Tac-Tics.