Three Dimension...

If $$P_1 : \overrightarrow{r} \cdot \overrightarrow{n_1} - d_1 = 0, P_2 : \overrightarrow{r} \cdot \overrightarrow{n_2} - d_2 = 0$$ and $$P_3 : \overrightarrow{r} \cdot \overrightarrow{n_3} - d_3 = 0$$ are three planes and $$\overrightarrow{n_1}, \overrightarrow{n_2}$$ and $$\overrightarrow{n_3}$$ are three non-copllanar vectors, then three lines $$P_1 = 0, P_2 = 0; P_2 = 0, P_3 = 0$$ and $$P_3 = 0, P_1 = 0$$  are

If $$L_1 = 0$$ is the reflected ray, then its equation is

If $$\cos {\alpha},\ \cos {\beta},\ \cos {\gamma}$$ are direction 
cosines of line, then the value of $$\sin^{2}\alpha + \sin^{2}\beta + 
\sin^{2}\gamma$$ is

If $$\cos {\alpha},\ \cos {\beta},\ \cos {\gamma}$$ are direction 
cosines of line, then the value of $$\sin^{2}\alpha + \sin^{2}\beta + 
\sin^{2}\gamma$$ is

If $$\alpha, \ \beta,\ \gamma$$ are direction angles of a line and $$\alpha = 60^{o},\ \beta=45^{o},\ \gamma =$$ ____.

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

The direction ratios of the line which is perpendicular to the two lines $$\dfrac{x-7}{2}=\dfrac{y+17}{-3}=\dfrac{z-6}{1}and\dfrac{x+5}{1}=\dfrac{y+3}{2}=\dfrac{z-6}{-2}$$ are

Te direction ratios of the line $$3x + 1 = 6 y - 2 = 1 -z $$ are 

Position vectors of two points are 
$$P(2\hat i+\hat j+3\hat k)$$ and $$Q(-4\hat i-2\hat j+\hat k)$$
Equation of plane passing through $$Q$$ and perpendicular of $$PQ$$ is 

which of the following group is not direction cosines of a line: