A displacement field in a titanium structure is given by:

$u=(x^2+10)({10}^{-4}),v=2yz({10}^{-4}),w=(-xy+z^2)({10}^{-4})$

$($a$)$ Check if the above displacement fields are compatible. Knowing that for titanium, $G=48$

GPa and $v=0\mathrm{.}33,$ determine the $($b$)$ state of strain and $($c$)$ state of stress at the point $P(2,2,0).$