Answer
$ \lt -0.39282 , 0.919615\gt and \lt 0.99282,-0.119615 \gt$
Work Step by Step
Two unit vectors that make an angle of $60^\circ$ with $v= \lt 3,4 \gt$
$x^2+y^2=1$
$x^2+((1/8)(5-6x))^2=1$
$100x^2-60x-39=0$
$x= \dfrac{3 \pm 4 \sqrt 3}{10} \approx -0.39282,0.99282$
and
$y=(1/8)(5-6x)\approx (1/8)(5-6(-0.39282))\approx 0.919615$
$y=(1/8)(5-6x)\approx (1/8)(5-6(0.99282))\approx -0.119615$
Hence, the two unit vectors are:
$ \lt -0.39282 , 0.919615\gt and \lt 0.99282,-0.119615 \gt$
