Question

Give a 4x4 matrix that rotates points in R^3 about the Z-axis through an angle -30*, and then translate by p=(5,-2,1)

Answer 1

@Loser66

Answer 2

wow, you go over me. I don't know how to solve it. hehehe...

Answer 3

okay thanks. Lol

Answer 4

How did you obtain it?

Answer 5

the combination of 3x3 rotation matrix about Z-axis through an angle -30 and translation p is defined by matrices:
\[\left[\begin{matrix}cos(-30)&-sin(-30)&0&5\\sin(-30)&cos(-30)&0&-2\\0&0&1&1\\0&0&0&1\end{matrix}\right]\]
\[=\left[\begin{matrix}\sqrt{3}/2&1/2&0&5\\-1/2&\sqrt{3}/2&0&-2\\0&0&1&1\\0&0&0&1\end{matrix}\right]\]

Answer 6

hopefully it's right. :)
@tkhunny

Answer 7

@mathmale @sourwing

Answer 8

^that looks right.

Answer 9

@Loser66

Answer 10

the translation matrix basically shift the whole entire object in 3D. It moves it from one position to another while the rotation in the translation matrix rotates the object about the z axis.

Answer 11

Actually I know nothing about it. Yesterday, when you made question, I made a short research about rotation matrix and the vector translation work on it. That gave you the matrix above. Today, I forgot what I did yesterday for the part I never study before like this. hehehe... I am so sorry.!!!

Answer 12

Hahaha no problem. THanks again!

Answer 13

@wilks311

Answer 14

You can do this, but can't do the pythag thm?! Dang dude. I'm lost lol.

Answer 15

when you get this high in math you tend to forget a lot of the basics. she didn't specify which leg was 6cm lol

Answer 16

Didn't matter, she specified the hypotenuse XD

but man, I'm in calc. Only matrices ive done have been 2D. 3D matrix bones me lol.

Answer 17

calc is easyXD

Answer 18

calc 1 was the easiest of them allXD

Answer 19

Yeah not saying it's hard. Just showing you that you giving me this problem is like giving a snake a pencil to use XD

Answer 20

LOL