If $ABCD$ is a parallelogram with $AC$ and $BD$ as diagonals,then which of the following is true regarding the vector relationship between the diagonals and sides?

Let $\vec{a}=2 \hat{i}+\hat{j}-\hat{k}$ and $\vec{b}=\hat{i}+3 \hat{j}-5 \hat{k}$ be two vectors,and $\overrightarrow{r}$ be a vector along the vector $3 \overrightarrow{a}-2 \overrightarrow{b}$ such that $|\overrightarrow{r}|=\sqrt{74}$. If the direction of $\vec{r}$ is opposite to that of $3 \vec{a}-2 \vec{b}$,then $\overrightarrow{r}=$

Find the unit vector in the direction of the vector $\vec{a} = \hat{i} + \hat{j} + 2\hat{k}$.

Find the unit vector in the direction of the sum of the vectors,$\vec{a}=2 \hat{i}+2 \hat{j}-5 \hat{k}$ and $\vec{b}=2 \hat{i}+\hat{j}+3 \hat{k}$.

If $a, b, c$ are any vectors,then the true statement is

$\bar{a}$ and $\bar{b}$ are non-collinear vectors. If $\bar{p} = (2x + 1)\bar{a} - \bar{b}$ and $\bar{q} = (x - 2)\bar{a} + \bar{b}$ are collinear vectors,then $x =$