Null space of a rank-one matrix

Let $A = \begin{pmatrix}a_1 & a_2 & a_3\ b_1 & b_2 & b_3\end{pmatrix}$ be a $2 \times 3$ real matrix, where $(a_1,a_2,a_3) \ne (0,0,0)$ and $(b_1,b_2,b_3) \ne (0,0,0)$. Assume that the rank of $A$ is 1. Define the subspaces $W = \{\mathbf{x} = \begin{pmatrix}x_1\\x_2\\x_3\end{pmatrix}\in\mathbb{R}^3 : A\mathbf{x} = \mathbf{0}\}$, $W_1 = \{\mathbf{x} = \begin{pmatrix}x_1\\x_2\\x_3\end{pmatrix}\in\mathbb{R}^3 : a_1x_1 + a_2x_2 + a_3x_3 = 0\}$ and $W_2 = \{\mathbf{x} = \begin{pmatrix}x_1\\x_2\\x_3\end{pmatrix}\in\mathbb{R}^3 : b_1x_1 + b_2x_2 + b_3x_3 = 0\}$. Consider the following statements: (I) $W = W_1 \cap W_2$ (II) $W_1 = W_2$ Which of the above statements is/are true?