Find the value of $x$ for which $x(\hat{i}+\hat{j}+\hat{k})$ is a unit vector.

$D, E, F$ are points on the sides $BC, CA$ and $AB$ of a $\triangle ABC$ respectively,dividing them in the ratios $2:3, 1:2, 3:1$ internally. The lines $BE$ and $CF$ intersect on the line $AD$ at $P$. If $\overrightarrow{AP} = x_1 \overrightarrow{AB} + y_1 \overrightarrow{AC}$,then $x_1 + y_1 =$

If a unit vector lies in the $yz$-plane and makes angles of $30^\circ$ and $60^\circ$ with the positive $y$-axis and $z$-axis respectively,then its components along the coordinate axes are:

If $\overline{e}_1, \overline{e}_2$ and $\overline{e}_1+\overline{e}_2$ are unit vectors,then the angle between $\overline{e}_1$ and $\overline{e}_2$ is (in $^{\circ}$)

If a point $C$ divides the line segment joining the points with the position vectors $2 \hat{i}-3 \hat{j}+2 \hat{k}$ and $3 \hat{i}-\hat{j}-2 \hat{k}$ in the ratio $2: 3$,then the distance of $C$ from the point with position vector $2 \hat{i}-\hat{j}+\hat{k}$ is

Answer the following as true or false.
$\vec{a}$ and $-\vec{a}$ are collinear.