Questions in 3-d

Select	Question
	If $A,B,C,D$are the points (2, 3, –1),(3, 5, –3), (1, 2, 3), (3, 5, 7) respectively, then the angle between AB and CD is
	The point of intersection of the lines $\frac{x-5}{3}=\frac{y-7}{-1}=\frac{z+2}{1},$ $\frac{x+3}{-36}=\frac{y-3}{2}=\frac{z-6}{4}$ is
	A line makes the same angle $\theta $, with each of the x and z–axis. If the angle $\beta $, which it makes with y-axis is such that ${{\sin }^{2}}\beta =3{{\sin }^{2}}\theta ,$then ${{\cos }^{2}}\theta $equals
	The angle between the lines $2x=3y=-z$ and $6x=-y=-4z$, is
	If the lines $\frac{x-1}{-3}=\frac{y-2}{2k}=\frac{z-3}{2}$, $\frac{x-1}{3k}=\frac{y-5}{1}=\frac{z-6}{-5}$ are at right angles, then $k =$
	The direction cosines of three lines passing through the origin are ${{l}_{1}},{{m}_{1}},{{n}_{1}};\,{{l}_{2}},{{m}_{2}},{{n}_{2}}$and ${{l}_{3}},{{m}_{3}},{{n}_{3}}$. The lines will be coplanar, if
	The distance of the point (2, 3, 4) from the line $1-x=\frac{y}{2}=\frac{1}{3}(1+z)$ is
	The angle between the straight lines $\frac{x-2}{2}=\frac{y-1}{5}=\frac{z+3}{-3}$and $\frac{x+1}{-1}=\frac{y-4}{8}=\frac{z-5}{4}$is
	The angle between the planes $3x-4y+5z=0$ and $2x-y-2z=5$ is
	The equation of the plane which is parallel to y-axis and cuts off intercepts of length 2 and 3 from x-axis and z-axis is