# Vectors in Mathematics

• Jul 27th 2009, 03:06 AM
brucycurlz
Vectors in Mathematics
Hey great pipz, i need help with mathematics vectors.
Here is an equation:
Vector (0,0) - (4,5), rotated 60 degress
Vectors including Rotate, Reflect and Translate (Wondering)
I need to know how to solve this problem. I would really appreciate your help.(Nod) Thanx
• Jul 27th 2009, 08:30 AM
apcalculus
Quote:

Originally Posted by brucycurlz
Hey great pipz, i need help with mathematics vectors.
Here is an equation:
Vector (0,0) - (4,5), rotated 60 degress
Vectors including Rotate, Reflect and Translate (Wondering)
I need to know how to solve this problem. I would really appreciate your help.(Nod) Thanx

The examples in 2D Graphics are the matrices you are looking for. Applying those matrices to your vector will achieve the wanted transformations.

Good luck!
• Jul 27th 2009, 11:32 AM
s_ingram
Hi Bracycurlz,

To solve this type of problem you need to calculate the image vector that arises by taking your initial vector v

$\displaystyle \left( \begin{array}{c} -4 \\ -5 \end{array} \right)$

and applying a transformation to it such that

v' = Tv

The transformation in this case will be a (2 x 2) matrix. There are transformations that translate, rotate, stretch and shear the original vector. So to rotate your vector by 60 degrees the Transformation matrix is

$\displaystyle \left ( \begin{array}{cc} cos \theta & sin \theta \\ sin \theta & cos \theta \end{array} \right)$

$\displaystyle \left ( \begin{array}{cc} \frac{1}{2} & \frac{-\sqrt{3}}{2} \\ \frac{\sqrt{3}}{2} & \frac{1}{2} \end{array} \right)$

I hope this helps.
• Jul 30th 2009, 02:45 AM
brucycurlz
Thanx
Thank u, but I'm think I'm still confussed about what's going on with mathematics vectors cause i didn't do the basics. Thnax and I'll c what i do.(Thinking)