Vector Spaces & Bases · Challenge problem

In $\mathbb{R}^4$ let $U = \operatorname{span}\{(1,0,1,0),\,(0,1,0,1),\,(1,1,0,0)\}$ and $W = \operatorname{span}\{(1,0,0,1),\,(0,1,1,0),\,(1,1,1,1)\}$. Find $\dim(U\cap W)$.