Problem $4.$ The displacement field in a $3$d body is given by$,$

$u=(x^2+2z){10}^{-3}$;$v=(3x+2y+2z){10}^{-3}$; and $w=(3z^2){10}^{-3}$

Compute change in the angle between two line segments $PQ$ and $PR$ at $P(2,1,3)$ having direction

cosine before deformation as

$PQ$: $l_1=0$;$m_1=n_1=\frac{1}{\sqrt[\phantom{2}]{2}}$

PR: $l_2=0\mathrm{.}6$;$m_2=0$;$n_2=0\mathrm{.}8$