Let $T: {\mathbb R}^3 \rightarrow {\mathbb R}^3$ be the linear transformation defined by $$T(x_1, x_2, x_3 )= (x_1- x_2, x_2- x_3, x_3-x_1).$$ Find a vector $\vec{w} \in {\mathbb R}^3$ that is NOT in the image of $T$. $\vec{w} =$ and find a different, nonzero vector $\vec{v} \in {\mathbb R}^3$ that IS in the image of $T$. $\vec{v} =$.