The unit vector in the direction of the vector $(1, 0, 0)$ is $.......$

If a vector $\vec{r}$ makes equal angles with the axes $OX, OY,$ and $OZ$,find the total number of such vectors $\vec{r}$.

$A$ and $B$ are two points. The position vector of $A$ is $6b - 2a$. $A$ point $P$ divides the line segment $AB$ in the ratio $1 : 2$. If $a - b$ is the position vector of $P$,then the position vector of $B$ is given by:

If $ABCDEFGH$ is a convex octagon,then $\vec{AB} + \vec{BC} + \vec{CD} + \vec{DE} + \vec{AH} + \vec{HG} + \vec{GF} + \vec{FE} = $

The sum of the lengths of projections of $p \hat{i} + q \hat{j} + r \hat{k}$ on the coordinate axes, where $p = 4, q = -5, r = 7$, is: (in $\text{ units}$)

If the position vectors of the vertices of a triangle are $a, b, c$,then find the sum of the vectors from the vertices to the centroid.