## Derivation of combined angle- Version 2

The simple analysis of combined angle (or compound angle) was described in this article.There the derivation was based on two deflection angles only. And hence the solution was approximate. For more accurate analysis, same approach can be used. The additional parameter included is the slope of incoming line.

However, a different approach which uses only coordinates can be used to calculate the actual deflection angle of two lines in 3D space. This approach will not only give the deflection angle but also provide accurate length of those lines.

Let us suppose three coordinates in space and let X be the angle between these two lines

A(x1,y1,z1)

B(x2,y2,z2)

C(x3,y3,z3)

The vector **AB** is given by

**AB**=(x2-x1)**i**+(y2-y1)**j**+(z2-z1)**k**

=(a1)**i**+(a2)**j**+(a3)**k**

Similarly BC is given by

**BC**=(x3-x2)**i**+(y3-y2)**j**+(z3-z2)**k**

=(b1)**i**+(b2)**j**+(b3)**k**

The dot product of vector is given by **AB.BC** =AB*BC*CosX

Here AB and BC=length of segment AB and BC respectively and is given by

L1=AB=sqrt(a1^2+a2^2+a3^2)

L2=BC=sqrt(b1^2+b2^2+b3^2)

Thus CosX=**AB.BC**/(L1*L2)

Total Lent of segment L=L1+L2

A worksheet using this approach can be **downloaded here. (combinedAngle_vectorMethod)** . The sheet also contains VBA codes to visualize the alignment.

### Like this:

Like Loading...

*Related*

or leave a trackback:

Trackback URL.

## Comments

You could definitely see your expertise in the article you

write. The arena hopes for even more passionate writers such as you who aren’t afraid to mention how they believe. Always go after your heart.

I truly wanted to post a simple comment so as to say thanks to you for those

stunning tips and hints you are writing on this website.

My particularly long internet research has at the end of the day been compensated

with good quality knowledge to talk about with my partners.

I would point out that many of us readers are very lucky to exist in a remarkable site with many

special individuals with very helpful opinions.

I feel really lucky to have used your entire site

and look forward to really more brilliant times reading here.

Thank you again for everything.