Which of the following statements is true?

The direction ratios of the line bisecting the angle between the $x$-axis and the line having direction ratios $(3, -1, 5)$ 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:

If $A(1, 0, 0)$,$B(0, 1, 0)$,and $C(0, 0, 1)$ are given,and $\vec{AB} = \vec{CX}$,then the point $X$ is:

If $2 \hat{i}+\hat{j}-\hat{k}$,$\hat{i}-3 \hat{j}+5 \hat{k}$ and $-3 \hat{i}+4 \hat{j}+4 \hat{k}$ are the position vectors of three points $A$,$B$ and $C$ respectively,then

The position vector of the point of intersection of the medians (centroid) of a triangle,whose vertices are $A(1, 2, 3)$,$B(1, 0, 3)$,and $C(4, 1, -3)$ is