# Matrix/projection of vectors problem

• May 5th 2011, 07:49 AM
karagorge
Matrix/projection of vectors problem
Another problem:

Use matrix multiplication to find the projection of the vectors (3,4) (2,1) and (-3,2) during rotation for -30 deg. with center in the coordinate start (beginning).

tnx
• May 5th 2011, 09:30 AM
HappyJoe
I don't see what your problem has to do with projections. Do you just want to find the images of the three vectors under a rotation of -30 degrees?
• May 5th 2011, 09:37 AM
karagorge
Yeah sorry bad translation - i meant the images of the three vectors.
• May 5th 2011, 09:52 AM
HappyJoe
It should appear somewhere in your book or in your notes that the matrix that rotates a vector through an angle of v is

cos(v), -sin(v)
sin(v), cos(v).

You can apply this to your specific problem.

(LaTeX won't work for me at the moment.)
• May 5th 2011, 10:09 AM
karagorge
Ok so it will look something like this:
1.
cos(-30) -sin(-30)
sin(-30) cos(-30)

and the matrix:
2.
3 2 -3
4 1 2
?

what should i do after - should i multiply 1. with 2.?

EDIT---
1.
-sqrt(3) / 2 , 1/2
-1/2 , -sqrt(3)/2
• May 5th 2011, 10:50 AM
HappyJoe
The matrix in 1. rotates vectors -30 degrees, right. You don't need the matrix in 2. for anything.

The way the matrix rotates a vector is simply by multiplying the matrix with the vector, so to see where (-3,2) gets rotated, you multiply the matrix in 1. with the column vector

-3,
2,

in that order.
• May 5th 2011, 10:53 AM
karagorge
tnx a lot for your help HappyJoe :)