If the direction cosines of a line are $\frac{1}{c}, \frac{1}{c}, \frac{1}{c}$,then:

If $\alpha, \beta, \gamma$ are the direction angles of a vector and $\cos \alpha = \frac{14}{15}$,$\cos \beta = \frac{1}{3}$,then $\cos \gamma = $

The coordinates of $P \equiv(1, 2, 3)$ and $O \equiv(0, 0, 0)$ are given. Find the direction cosines of $\overline{OP}$.

$A$ line makes angles $\alpha, \beta, \gamma$ and $\delta$ with the diagonals of a cube. Prove that $\cos^{2} \alpha + \cos^{2} \beta + \cos^{2} \gamma + \cos^{2} \delta = \frac{4}{3}$.

$A$ line $AB$ in three dimensions makes angles $45^{\circ}$ and $120^{\circ}$ with the positive $X$-axis and the positive $Y$-axis respectively. If $AB$ makes an acute angle $\theta$ with the positive $Z$-axis,then $\theta$ equals (in $^{\circ}$)

If $l_1, m_1, n_1$ and $l_2, m_2, n_2$ are direction cosines of $OA$ and $OB$ such that $\angle AOB = \theta$,where $O$ is the origin,then the direction cosines of the internal angular bisector of $\angle AOB$ are