Simplify the following. Your answers: = + 2 + t = + 2t + z

The vector equation is given as $\vec{AC} = \vec{AB} + \vec{BC}$. This is a standard vector addition following the triangle rule, where the head of $\vec{AB}$ connects to the tail of $\vec{BC}$ to form $\vec{AC}$. The student has assigned the algebraic expression $z+t$ to this.

The expression $z+t$ consists of two distinct variables, $z$ and $t$. Without further information or values for these variables, this expression is already in its simplest form.

The vector equation is given as $\vec{DB} = \vec{DA} + \vec{AB}$. This also follows the triangle rule for vector addition. The student has assigned the algebraic expression $2t+z$ to this.

The expression $2t+z$ consists of two distinct variables, $t$ and $z$, with $t$ having a coefficient of 2. This expression is already in its simplest form.