If the points $P(3,\mu,6), Q(-1,-1,2)$ and $R(2,8,5)$ are collinear, then the value of '$\mu$' is

If lines $\frac{x+5}{5\lambda+2} = \frac{4-2y}{10} = \frac{1-3z}{-3}$ and $\frac{x-2}{1} = \frac{1+2y}{4\lambda} = \frac{2+z}{3}$ are perpendicular, than value of '$\lambda$' is

Points on the line $\frac{x+2}{3} = \frac{y+1}{2} = \frac{z-3}{2}$ at a distance of 5 units from the point $(1, 3, 3)$, are

If $\lambda$ and $\mu$ are parameters, then

Match the LIST-I with LIST-II

Choose the correct answer from the options given below:

Let ABCD be a parallelogram with vertices $A(2,2,a), B(1,0,0), C(1,3,a)$ and D, where $a > 0$. If the area of parallelogram is 5 square units, then the value of $a$ is:

The shortest distance between the following lines:

$\vec{r} = (\hat{i} + \hat{j} - \hat{k}) + s(2\hat{i} + \hat{j} + \hat{k})$

$\vec{r} = (\hat{i} + \hat{j} + 2\hat{k}) + t(4\hat{i} + 2\hat{j} + 2\hat{k})$, where s and t are scalars, is:

The reflection of the point $(\alpha, \beta, \gamma)$ in the xz plane is