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 $|\overline{a}|=2, |\overline{b}|=3, |\overline{c}|=5$ and each of the angles between the vectors $\overline{a}$ and $\overline{b}$,$\overline{b}$ and $\overline{c}$,and $\overline{c}$ and $\overline{a}$ is $60^{\circ}$,then the value of $|\overline{a}+\overline{b}+\overline{c}|$ is

In a quadrilateral $ABCD$,the point $P$ divides $DC$ in the ratio $1:3$ internally and $Q$ is the mid-point of $AC$. If $\vec{AB} + \vec{AD} + \vec{BC} - 2\vec{DC} = \lambda \vec{PQ}$,then the value of $\lambda$ is

In a triangle $ABC$,if $2\overrightarrow{AC} = 3\overrightarrow{CB}$,then $2\overrightarrow{OA} + 3\overrightarrow{OB}$ equals

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

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