The angle between the lines,whose direction cosines $l, m, n$ satisfy the equations $l+m+n=0$ and $2l^2+2m^2-n^2=0$,is (in $^{\circ}$)

Let $\alpha$ be the angle between the lines whose direction cosines satisfy the equations $l+m-n=0$ and $l^{2}+m^{2}-n^{2}=0$. Then the value of $\sin^{4} \alpha + \cos^{4} \alpha$ is

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?

Let $O$ be the origin and $P$ be a point which is at a distance of $3$ units from the origin. If the direction ratios of $\vec{OP}$ are $(1, -2, -2)$,then the coordinates of $P$ are

If $l_1, m_1, n_1$; $l_2, m_2, n_2$ and $l_3, m_3, n_3$ are the direction cosines of three mutually perpendicular lines,find the direction cosines of a line that makes equal angles with these lines.

The lines whose direction cosines are given by the relations $a l+b m+c n=0$ and $m n+n l+l m=0$ are