Three Dimensional Geometry

The magnitude of projection of line joining $(3,4$, $5)$ and $(4,6,3)$ on the line joining $(-1,2,4)$ and $(1,0,5)$ is

Let the acute angle bisector of the two planes $x-2 y-2 z+1=0$ and $2 x-3 y-6 z+1=0$ be the plane $P$. Then which of the following points lies on P?

The angle between the lines whose direction cosines are given by the equations $3 l+m+5 n=$ $0,6 \mathrm{~nm}-2 \mathrm{n} l+5 l \mathrm{m}=0$ is

The shortest distance between the lines $\mathrm{x}=\mathrm{y}+$ $2=6 z-6$ and $x+1=2 y=-12 z$ is

If the straight lines $\frac{x-1}{k}=\frac{y-2}{2}=\frac{z-3}{3}$ and $\frac{x-2}{3}=\frac{y-3}{k}=\frac{z-1}{2}$ intersect at a point, then the integer $\mathrm{k}$ is equal to

If the co-ordinates of the point in which the line joining the points $(3,5,-7)$ and $(-2,1,8)$ is intersected by the plane $y z$ is $\left[\mathrm{a}, \frac{13}{\mathrm{~b}}, \mathrm{c}\right]$, then $(a+b-c)=$

The shortest distance between the lines $\frac{x-3}{2}=\frac{y-2}{3}=\frac{z-1}{-1}$ and $\frac{x+3}{2}=\frac{y-6}{1}=\frac{z-5}{3}$ is :

The lines $\frac{x-2}{1}=\frac{y-3}{1}=\frac{z-4}{-k}$ and $\frac{x-1}{k}=\frac{y-4}{2}=\frac{z-5}{1}$ are coplanar if

If the plane $3 x+y+2 z+6=0$ is parallel to the line $\frac{3 x-1}{2 b}=3-y=\frac{z-1}{a}$, then the value of $3 a+3 b$ is

A line makes angles of $45^{\circ}$ and $60^{\circ}$ with the positive axes of $X$ and $Y$ respectively. The angle made by the same line with the positive axis of $Z$, is

The length of the perpendicular drawn from the point $(3,-1,11)$ to the line $\frac{x}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ is :

The distance from the point (3,4,5) to the point where the line $\frac{x-3}{1}=\frac{y-4}{2}=\frac{z-5}{2}$ meets the plane $x+y+z=17$ is