Let U and W be orthogonal subspaces

1) prove that U $\displaystyle \bigcap$ W = {0}

2) if {$\displaystyle u_1,u_2,....u_m$ }is a linearly independent subset of U and {$\displaystyle w_1,w_2,...w_n $}is a linearly independent subset of W, prove that {$\displaystyle u_1,u_2,....,u_m, w_1,w_2,...,w_n$} is a linearly independent set in V.