If the direction cosines of two lines are given by $l+m+n=0$ and $l^2-5m^2+n^2=0$, then the angle between them is

$A$ vector $v$ is equally inclined to the $x$-axis,$y$-axis,and $z$-axis respectively. Its direction cosines are:

If $\cos \alpha, \cos \beta, \cos \gamma$ are the direction cosines of a vector $\vec{a}$,then $\cos 2 \alpha + \cos 2 \beta + \cos 2 \gamma$ is equal to

Let $A(1,-1,2), B(6,11,2), C(1,2,6)$ be three points. If $l_1, m_1, n_1$ are the direction cosines of $AB$ and $l_2, m_2, n_2$ are the direction cosines of $AC$,then $|l_1 l_2+m_1 m_2+n_1 n_2|=$

The coordinates of the point $P$ are $(x, y, z)$ and the direction cosines of the line $OP$ where $O$ is the origin $(0, 0, 0)$ are $l, m, n$. If $r$ is the distance $OP$,then which of the following relations is correct?

If the distance between two points $A$ and $B$ is $d$, and the lengths of the projections of $AB$ on the coordinate planes are $d_1, d_2, d_3$, then