The direction cosines of two lines are $\langle\frac{\sqrt{3}}{2}, \frac{1}{4}, \frac{\sqrt{3}}{4}\rangle$ and $\langle-\frac{\sqrt{3}}{2}, \frac{1}{4}, \frac{\sqrt{3}}{4}\rangle$. Then the angle between the lines is equal to (in $^{\circ}$)

If the direction ratios of a line are proportional to $1, 2, 3$,find the projection of the line segment joining the points $(5, 2, 3)$ and $(-1, 0, 2)$ on the line.

If the direction cosines of a straight line are $\left(\frac{1}{c}, \frac{1}{c}, \frac{1}{c}\right)$,then $c$ is equal to

If the direction ratios of a line are $1, -3, 2$,then the direction cosines of the line are

The direction cosines of the line passing through $P(2, 3, -1)$ and the origin $O(0, 0, 0)$ are:

Suppose $(l_1, m_1, n_1)$ and $(l_2, m_2, n_2)$ are the direction cosines of two lines and $\theta$ is the angle between them,where $\cos \theta = \pm(l_1 l_2 + m_1 m_2 + n_1 n_2)$. Let $A=(1, -2, 3)$,$B=(3, 1, -3)$,and $C=(-3, 1, 3)$ be the vertices of $\triangle ABC$. Then,$\cos A =$