Determine the structural stiffness matrix $K$ for the $3-$member truss shown below. $$ is an acute angle. Use the given destination vectors for member numbering and orientation

Use trigonometry to show final solution in terms of $sin$ and $cos$ wherever applicable. Do nor leave results half calculated such as $sin(-),cos(-),$ ctc$.$

Given:

Member $1$: $A_1,E_1,L_1$

Member $2$: $A_2,E_2,L_2$

Member $3$: $A_3,$ Es$,L_s$

dvec $=\left[\begin{array}{ccc}0& 0& 0\\ 0& 1& 0\\ 0& 2& 2\\ 1& 0& 0\end{array}\right]$