The angle between the pair of lines with direction ratios $1, 1, 2$ and $\sqrt{3}-1, -\sqrt{3}-1, 4$ is $... ^\circ$.

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,$\cos A =$

The distance between two points $P$ and $Q$ is $d$ and the lengths of the projections of $PQ$ on the coordinate planes are $d_1, d_2, d_3$. Then $d_1^2 + d_2^2 + d_3^2 = k d^2$,where $k$ is:

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

If $OA$ is equally inclined to $OX, OY$ and $OZ$ and if $A$ is $\sqrt{3}$ units from the origin, then $A$ is:

If the direction cosines of two lines are such that $l+m+n=0$ and $l^2+m^2-n^2=0$, then the angle between them is