Q: I need to find two unit vectors 60 degrees from the vector <3,4>.
What I did was say the unit vector u= is one of my solutions and so
\(\overrightarrow{v}\cdot\overrightarrow{u}=3x+4y\) , \(|\overrightarrow{v}|=\sqrt{3^2+4^2}=5\) , \(|\overrightarrow{u}|=1\)
\(3x+4y=5cos(60^{\circ})\)
\(\frac{6}{5}x+\frac{8}{5}y=0 \)
\(\frac{6}{5}x=-\frac{8}{5}y\)
\(x=\frac{-3}{4}y\)
Now they need to be unit vectors so the intersection of this line with the circle at the origin of radius 1. The resulting two vectors do not seem to be 60 degrees from the given vector! why, what did I do wrong and what should I do?
