If $\vec{a} = \vec{b}$,then............

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?

If the position vectors of $A$ and $B$ are respectively $(1, 1, 0)$ and $(0, 1, 1)$,then $\overrightarrow{AB} =$

The zero vector $(0,0,0)$ $........$

If non-zero vectors $\vec{a}$,$\vec{b}$,and $\vec{c}$ are related by $\vec{a} = 8\vec{b}$ and $\vec{c} = -7\vec{b}$,find the angle between $\vec{a}$ and $\vec{c}$.

If $\vec{a} = \hat{i} + 2\hat{j} + 3\hat{k}$,$\vec{b} = 2\hat{i} + 3\hat{j} + \hat{k}$,$\vec{c} = 3\hat{i} + \hat{j} + 2\hat{k}$ and $\alpha \vec{a} + \beta \vec{b} + \gamma \vec{c} = -3(\hat{i} - \hat{k})$. Then the triplet $(\alpha, \beta, \gamma)$ is