IJK vs XYZ

[[Ja...]]

Can someone help differentiate I,J,K versus X,Y,Z for me? Most of the articles I've read are WAY over my head, but it seems as if X,Y,Z denotes the location of a point, whereas I,J,K denotes the direction. Is that somewhat accurate, in layman's terms?

[[Mi...]]

Basically, yes.

The direction vector ijk represent is a unit vector (meaning it has a length of 1), and the i, j and k values are its x, y and z components, respectively.

[[Se...]]

Here's a little diagram that can help you visualize how it works:

As Michael said, the length of the vector is 1 and i j k are the coordinates of this vector on the x y z axes.
Knowing the angle of the vector you only need a little trigonometry to calculate their values...

[[To...]]

Ref:
Cos 0° = 1
Cos 90° = 0

So, using a point with a vector in the +Z direction, the angle relationship to the Z axis is 0°, so the k value equals 1. The angle relationship to X and Y is 90°, so the i and j equal 0

[[Ow...]]

I remember a time I calculated everything by the formula in a book or hundreds of pages of notes I'd taken. Then I got a Texas-instrument smart calculator you could store formula programs in (actually had one before a computer), then items like the attached and now engineering cadworks or internet. I guess you'd have to be on the older side of life to truly realize how technology has made things so much quicker.
Anyhow,
Attached is an excel document with all kinds of info and calculators for vector, bolt pattern, angle, ext...

Direction Vector Calculator.xls

[[Ja...]]

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Thank you, Owen! I'm 34, so just young enough to rely on technology, but old enough to appreciate the time before it ruled us. That spredsheet is VERY informative, if not a bit daunting. It seems like I,J,K becomes important when measuring angled surfaces from what I can tell. I usually create an alternate alignment that levels to the surface in question to help circumvent this. However, understanding what vectors and I,J,K is/are is crucial to becoming better at what I do.

[[Is...]]

For 3D vectors you need to calculate a little bit more..

Points=""
sphereRadius=20
measPlane =15
for n = 1 To 360	
Points=Points+  formatR(((sphereRadius**2 - measPlane**2)**(1/2)) *cos(n),0,10)+ "    " +  formatR(((sphereRadius**2 - measPlane**2)**(1/2)) *sin(n),0,10) + "    " + formatR(measPlane,0,10)  + "    " + formatR((cos(n)*cos(arcsin(measPlane/sphereRadius))),0,10)+ "    " +  formatR((sin(n)*cos(arcsin(measPlane/sphereRadius))),0,10) + "    " + formatR(sin(arcsin(measPlane/sphereRadius)),0,10)  + "    " + "0.0" + cr() 
next n
deleteFile("Points.txt")
addToFile("Points.txt", "   x          	   y          	   z          	   u          	   v          	   w          	    r         " + cr() + Points )