Question

come up with vector u and v, with u parallel to y and v perpendicular to y and x= u+v. Y=(cos(pi/6), sin(pi/6)), x= 3(cos(pi/3),sin(pi/3))

Answer 1

"u parallel to y"
means that \[\vec u\cdot\vec y=\|\vec u\|\|\vec y\|\]so take the dot product on the left and multiply the magnitudes right, will get you one equation

"v perpendicular to y and x"
means that\[\vec u\cdot\vec y=\vec v\cdot\vec x=0\](the dot product of two perpendicular vectors is zero)
so do the dot product; that will give you another equation
use the system of two equations and solve for the components of \(\vec u\) and \(\vec v\)

Answer 2

i got u=(\[(-9\sqrt{3}+18)(\sqrt{3}/2,1/2)\]
V=(\[16-9\sqrt{3},27-16\sqrt{3}\])

Answer 3

is that correct?