If $a = i + 2j + 3k$,$b = -i + 2j + k$ and $c = 3i + j$,then the unit vector along their resultant is:

If $\vec{a}=(2x+y)\hat{i}+3\hat{j}+9\hat{k}$ and $\vec{b}=2\hat{i}+\hat{j}-(x-y)\hat{k}$ are two collinear vectors,then $x^3+27y^3=$

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:

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

In a regular hexagon $ABCDEF$,$AD + EB + FC = (3\lambda - 8) AB$. Then $\lambda =$

If the sum of two unit vectors is a unit vector,then the magnitude of their difference is