Calculate a vector wich forma an angle alpha with another vector

[germangb]

Homework Statement

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

Thank you very much

Homework Equations

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

thanks

 

[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.

 

[germangb]

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