If $ABCDEF$ is a regular hexagon and $\overrightarrow{AB} + \overrightarrow{AC} + \overrightarrow{AD} + \overrightarrow{AE} + \overrightarrow{AF} = \lambda \overrightarrow{AD}$,then $\lambda = $

If $L, M, N$ are the midpoints of the sides $PQ, QR$ and $RP$ of $\triangle PQR$ respectively,then $\overrightarrow{QM} + \overrightarrow{LN} + \overrightarrow{ML} + \overrightarrow{RN} - \overrightarrow{MN} - \overrightarrow{QL} = $

If the points whose position vectors are $2 \hat{i}+\hat{j}+\hat{k}$, $6 \hat{i}-\hat{j}+2 \hat{k}$, and $14 \hat{i}-5 \hat{j}+p \hat{k}$ are collinear, then the value of $p$ is:

The position vectors of three points $A, B$ and $C$ are $(1, 3, x), (3, 5, 8)$ and $(y, -1, -6)$ respectively. If $A, B$ and $C$ are collinear, then $(x, y) =$

If $D, E$ and $F$ are respectively the mid-points of $AB, AC$ and $BC$ in $\triangle ABC$, then $\overrightarrow{BE} + \overrightarrow{AF}$ is equal to :

The position vectors of the points $A, B, C$ are $(2i + j - k)$,$(3i - 2j + k)$,and $(i + 4j - 3k)$ respectively. These points