# 3D Math Primer... By F. Dunn & I. Parberry question

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Hey guys, I am reading 3D Math Primer for Graphics and Game Development from this site http://www.scribd.com/doc/11997032/3D-Math-Primer-for-Graphics-and-Game-Development. I got to point 5.8.2, and I understand that if you add 2 vectors together you will get another vector (triangle rule). For figure 5.7 with more than 2 vectors I was wondering how would you get the total distance that you would have traveled from beginning to end? I don't want the vector that connects them together. What I think is that I have to work out the magnitude for each individual vector and then add them altogether to get the answer. Would that be correct? I hope I've worded it right :)

Correct.

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Hey guys,

I am up to Chapter 8, section 8.2.3 - Rotation About An Arbitrary Axis

And this part here...

I am having trouble understanding the maths on those 2 lines where I've shaded with a rectangle.

How is n times v parallel = zero?

Thanks guys.

Appreciate the help always :-D

BTW the on-line for the text is http://www.scribd.com/doc/11997032/3D-Math-Primer-for-Graphics-and-Game-Development

[Edited by - tenpoundbear on February 27, 2010 2:58:47 AM]

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I might be wrong, but:

On p. 109, they write "Since v|| is parallel to n ...", which can also be seen from figure 8.12 on p. 110. Now, from the associative property of the cross product, we have $k(\bold{a} \times \bold{b}) = (k\bold{a}) \times \bold{b} = \bold{a} \times (k\bold{b})$ (see p. 66). However, at p. 110, it is clear that $\bold{v}_{\parallel} = (\bold{v} \cdot \bold{n})\bold{n}$. In other words, $\bold{v}_{\parallel}$ is a vector with magnitude $(\bold{v} \cdot \bold{n})$, and direction $\bold{n}$ (a scalar times a vector).

If we plug this into the cross product, we get $(\bold{n} \times \bold{v}_{\parallel}) = (\bold{n} \times (\bold{v} \cdot \bold{n})\bold{n} = (\bold{v} \cdot \bold{n})(\bold{n} \times \bold{n})$. Finally, we apply the fact that $(\bold{a} \times \bold{a}) = 0$
, which you may check on p. 66 as well. Thus, we have that $(\bold{n} \times \bold{v}_{\parallel}) = (\bold{v} \cdot \bold{n})(\bold{n} \times \bold{n}) = 0$.

Edit: updated with LaTeX eqs for improved readability.

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First of all, please don't say v times n. Please use cross (in this case), or dot, box, perpdot, resp., in the other cases. That avoids confusion, IMHO.

Now, coming to the problem. I assume it is clear that the first formulas shown decompose the vector v into 2 vectors that in sum gives
v = v + v||
where
v is perpendicular to n and
v|| is parallel to n.

The cross-product computes a vector that is perpendicular to both of its argument vectors, and its length is proportional to the sine of the included angle:
|v1 x v2| == |v1| * |v2| * sin( <v1,v2> )

But due to how v|| is computed, it is parallel to n, so that the included angle is 0, and hence the sine is zero, and hence the resulting vector has length 0. The only vector that has zero length is the zero vector 0.

The vector resulting from a cross product has its maximum length (assuming that the both argument vectors have a given length) when the included angle is 90°. If the angle is made smaller (or greater) then the resulting vector shrinks until it reaches length 0 at 0° (or 180°).

[Edited by - haegarr on February 27, 2010 3:51:50 AM]

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Hi Guys,

I think I read the equation incorrectly, I thought the 'X' was a multiplication symbol but its a cross product.

So I think I understand it now.

Sorry about using the incorrect term haegarr, I may have to research how to type those mathematical symbols next time I post.

Anyways, the maths is getting a bit heavy from chapter 8 onwards. I think I will come back to this text once I am more knowledgeable.

Thanks heaps guys.

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