# Vector problem

Geometry Level 3

The vector $$\overrightarrow { F }$$ is the sum of vectors $$\overrightarrow { { f }_{ 1 } }$$ and $$\overrightarrow { { f }_{ 2 } }$$ such that $$\sphericalangle \quad (\overrightarrow { { f }_{ 1 } } ,\overrightarrow { { f }_{ 2 } } )\quad =\quad 60°$$ and $$|\overrightarrow { { f }_{ 1 } }| : |\overrightarrow { { f }_{ 2 } }| \quad =\quad 2:3$$. Let $$x$$ = the angle enclosed by $$\overrightarrow { { f }_{ 1 } }$$ and $$\overrightarrow { F }$$, and let $$y$$ = the angle enclosed by $$\overrightarrow { { f }_{ 2 } }$$ and $$\overrightarrow { F }$$ (both in degrees). Find the value of $$y-x$$ correct to 3 significant figures.