In a $\triangle ABC$ (shown in the figure below),state whether the following are true or false:
$(i)$ $\vec{AB} + \vec{BC} + \vec{CA} = \vec{0}$
(ii) $\vec{AB} + \vec{BC} - \vec{AC} = \vec{0}$
(iii) $\vec{AB} - \vec{CB} + \vec{CA} = \vec{0}$
(iv) $\vec{AB} + \vec{BC} - \vec{CA} = \vec{0}$

$ABCD$ is a parallelogram such that $L$ is the mid-point of $BC$. Then,$\vec{AL}$ is equal to:

For a triangle $ABC$,if $\vec{AB} = 3\hat{i} + 4\hat{k}$ and $\vec{AC} = 5\hat{i} - 2\hat{j} + 4\hat{k}$,then the length of the median drawn from vertex $A$ is:

For any two points $M$ and $N$ in the $XY$-plane, let $\overrightarrow{MN}$ denote the vector from $M$ to $N$, and $\overrightarrow{0}$ denote the zero vector. Let $P, Q$ and $R$ be three distinct points in the $XY$-plane. Let $S$ be a point inside the triangle $\triangle PQR$ such that $\overrightarrow{SP} + 5\overrightarrow{SQ} + 6\overrightarrow{SR} = \overrightarrow{0}$. Let $E$ and $F$ be the mid-points of the sides $PR$ and $QR$, respectively. Then the value of $\frac{\text{length of the line segment } EF}{\text{length of the line segment } ES}$ is: (in $.20$)

Find the vector joining the points $P(2, 3, 0)$ and $Q(-1, -2, -4)$ directed from $P$ to $Q$.

If $\vec{a} = 2\hat{i} - 3\hat{j} + 4\hat{k}$ and $\vec{b} = \hat{i} + 2\hat{j} - \hat{k}$,then $\vec{a} + \vec{b} = \dots$