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.

Note. Answer should be positive.

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