The unit vector parallel to the resultant vector of $2i + 4j - 5k$ and $i + 2j + 3k$ is

If the vectors $\vec{a}=2 \hat{i}+p \hat{j}+4 \hat{k}$ and $\vec{b}=6 \hat{i}-9 \hat{j}+q \hat{k}$ are collinear,then the values of $p$ and $q$ are:

The components of a vector $\vec{a}$ with respect to a rectangular Cartesian system are $2p$ and $1$. The system is rotated about the origin through a certain angle in the counter-clockwise direction. If the components of $\vec{a}$ with respect to the new system are $p + 1$ and $1$,then:

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

If $\vec{a}, \vec{b}, \vec{c}$ are position vectors of points $A, B, C$ respectively,with $2 \vec{a}+3 \vec{b}-5 \vec{c}=\vec{0}$,then the ratio in which point $C$ divides segment $AB$ is

$I$. Two non-zero, non-collinear vectors are linearly independent.
$II$. Any three coplanar vectors are linearly dependent.
Which of the above statements is/are true?