Suppose I have two sets of linearly independent 3-d vectors denoted by $W=\{\vec{w_1},\vec{w_2},\vec{w_3}\}$ and $V=\{\vec{v_1},\vec{v_2},\vec{v_3}\}$ and then construct two unbounded conic hull,
$C_w=c_1\vec{w_1}+c_2\vec{w_2}+c_2\vec{w_2}$
$C_v=d_1\vec{v_1}+d_2\vec{v_2}+d_2\vec{v_2}$
for $c_i,d_i \in \mathbb{R}_{+}$. Then how can one algebraically find if the two conic hulls intersect or not? simply from the knowledge of the basis vectors $w_i$ and $v_i$. Any matrix equation or any other quick method?