Let $H=$Span$\{v_1,v_2\}$ and $K=$Span$\{v_3,v_4\},$ where $v_1,v_2,v_3,$ and $v_4$ are given below.

$v_1=\left[\begin{array}{c}1\\ 6\\ 7\end{array}\right],v_2=\left[\begin{array}{c}2\\ 6\\ 8\end{array}\right],v_3=\left[\begin{array}{c}6\\ -1\\ 1\end{array}\right],v_4=\left[\begin{array}{c}0\\ -36\\ -12\end{array}\right]$

Then $H$ and $K$ are subspaces of $R^3.$ In fact, $H$ and $K$ are planes in $R^3$ through the origin, and they intersect in a line through $0.$ Find a nonzero vector $w$ that generates $t$

$w=$

$[$Hint: $w$ can be written as $c_1{v}_1+c_2{v}_2$ and also as $c_3{v}_3+c_4{v}_4$ To build $w,$ solve the equation $c_1{v}_1+c_2{v}_2=c_3{v}_3+c_4{v}_4$ for the unknown $c_9\text{'}$s$.]$