Calculate a vector wich forma an angle alpha with another vector

1. Jul 21, 2012

germangb

1. The problem statement, all variables and given/known data

Looks very simple, but I need help.
I have a 2D vector, v, and I need to calculate a vector wich forms an angle $\alpha$ with it.

Thank you very much

2. Relevant equations

I think that the equations should be, for 2 given vector u and v:

thanks

Last edited: Jul 21, 2012
2. Jul 21, 2012

HallsofIvy

There are, of course, an infinite number of such vectors- of different lengths as well as on either side of u. If you are given vector $\vec{u}= u_x\vec{i}+ u_y\vec{j}$, taking $\vec{v}= v_x\vec{i}+ v_y\vec{v}$, then we must have, as you say, $v_xu_x+ v_yu_v= \sqrt{u_x^2+ u_y^2}cos(\alpha)$.

There is no "$\sqrt{v_x^2+ v_y^2}$" in that because I have decided, for simplicity, to look for a unit vector making angle $\alpha$ with $\vec{u}$. And, of course, that means that $v_x^2+ v_y^2= 1$.

Solve those two equations for $u_x$ and $u_y$.

3. Jul 21, 2012

germangb

thanks for the help, HallsofIvy, now I see my error. I wasn't using the second equation