Three Dimension...

The angle between the lines $$2x=3y=-z$$ and $$6x=-y=-4z$$ is 

If a line makes an angle of $${\pi }/{4}$$ with the positive direction of each of $$x$$-axis and $$y$$-axis, then the angle that the line makes with the positive direction of the $$z$$-axis is

The line passing through the points $$(5,1,a)$$ and $$(3,b,1)$$ crosses the $$yz$$-plane at the point $$\left (0,\dfrac {17}{2}, \dfrac {-13}{2}\right)$$, then 

A line $$AB$$ in three-dimensional space makes angles $$45^{\mathrm{o}}$$ and $$120^{\mathrm{o}}$$ with the positive $$\mathrm{x}$$-axis and the positive $$\mathrm{y}$$-axis respectively. lf $$AB$$ makes an acute angle $$e$$ with the positive $$\mathrm{z}$$-axis, then $$e$$ equals

A line in the 3-dimensional space makes an angle $$\theta \left(0 < \theta \leq \dfrac {\pi}{2}\right)$$ with both the x and y axes, then the set of all values of $$\theta$$ is the interval :

A line makes the same angle $$\Theta$$, with each of the $$\mathrm{x}$$ and $$\mathrm{z}$$ axis. If the angle $$\beta$$, which it makes with $$\mathrm{y}$$-axis, is such that $$\sin^{2}\beta=3\sin_{\Theta}^{2}$$, then $$\cos^{2}\Theta$$ equals: 

A line with positive direction cosines passes through the point $$P(2, -1, 2)$$ and makes equal angles with the coordinate axes. The line meets the plane $$2x + y + z = 9$$ at point $$Q$$. The length of the line segment $$PQ$$ equals

If the lines $$\dfrac{x-2}{1}=\dfrac{y-3}{1}=\dfrac{z-4}{-k}$$ and $$\dfrac{x-1}{k}=\dfrac{y-4}{2}=\dfrac{z-5}{1}$$ are coplanar, then $$k$$ can have 

If the straight lines $$\displaystyle \dfrac{x-1}{2}=\dfrac{y+1}{K}=\dfrac{z}{2}$$ and $$\displaystyle \dfrac{x+1}{5}=\dfrac{y+1}{2}=\dfrac{z}{K}$$ are coplanar, then the plane(s) containing these two lines is(are)

The points with position vectors $$60 \widehat{i} + 3 \widehat{j}$$, $$40 \widehat{i} - 8 \widehat{j}$$, $$a\widehat{i} -52\widehat{j}$$ are collinear if