The projection of the line segment joining the points $(2,1,-3)$ and $(-1,0,2)$ on the line whose direction ratios are $3,2,6$ is

The direction cosines of the line $\frac{3x + 1}{-3} = \frac{3y + 2}{6} = \frac{z}{-1}$ are

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

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

Let $P(x, y, z)$ be a point in the first octant,whose projection in the $xy$-plane is the point $Q$. Let $OP = \gamma$; the angle between $OQ$ and the positive $x$-axis be $\theta$; and the angle between $OP$ and the positive $z$-axis be $\phi$,where $O$ is the origin. Then the distance of $P$ from the $x$-axis is:

The projection of the line segment joining $P(2, -1, 0)$ and $Q(3, 2, -1)$ on the line whose direction ratios are $1, 2, 2$ is