Further 3d vector calculation question...?

Question

I'm slowly starting to understand 3d vectors. I hope someone can explain further.

I'm trying to calculate the angles between 8 lines in 3D space. I have the start and end point of each line as a 3d vector. A previous suggestion was:

"You first need to write each one as a unit vector, which means dividing all of the values through by a value so that the magnitude will be 1. For each of these vectors, this means dividing by the length of the vector."

That makes sense, I think. Can someone check my sums to be sure I'm doing it

For example, here is the first set of points:

From: 0.0548981, -0.0473777, -0.12331
To: 0.0595451, -0.0757554, -0.055356

So...
Endpoint minus start point:
0.0595451, -0.0757554, -0.055356

Gives vector length 0.073787767

So the unit vector is:
0.062977919, -0.384585428, 0.92093856

Is that correct?

Where do I go from here?

Modulo wrote:

"Use properties of dot product to get angles.

v1*v2 = |v1|*|v2|*cos(theta)

If you first normalize your vectors then |v| = 1 it makes the calculations"


I'm sorry, I'm from a medical background. Can someone please explain how to normalize my vectors.

Pretend you're talking to a dummy ;-)

Answer 1

Use properties of dot product to get angles.

v1*v2 = |v1|*|v2|*cos(theta)

If you first normalize your vectors then |v| = 1 it makes the calculations easier.

Answer 2

It's decades since I taught this, but if I remember correctly, what you have calculated is called the direction cosines for the vector. Again, if I remember correctly, to find the angle between two lines you have to multiply their direction cosines together, i.e. if the two sets of cosines are (a1, b1, c1) and (a2, b2, c2), you work out
a1*a2 + b1*b2 + c1*c2, but of course that isn't the angle; it may be the sine or cosine or something else, but you must have that somewhere in a book or notes and can look it up.

PS "normalising vectors" is what you did when you divided the three components of the vector by the length. And what the first answerer said suggests that after you've multiplied the direction cosines together you have the cosine of the angle between the lines, so you just do inverse cosine.

Answer 3

the version between a three-D and a 2 D merchandise is that a three-D could nicely be seen from all factors of the determine. A 2nd is merely your commonly used photograph.3-D gadgets are usually built out of wood, clay, or any development fabric. 2nd gadgets are drawn on a peice of paper. the large concern approximately 3-D is that a individual can get the popular thought that its actual.