If the line passes through the points $P(6, -1, 2)$,$Q(8, -7, 2\lambda)$,and $R(5, 2, 4)$,then the value of $\lambda$ is $.......$

The lines $\frac{x - 1}{2} = \frac{y - 1}{2} = \frac{z - 3}{0}$ and $\frac{x - 2}{0} = \frac{y - 3}{0} = \frac{z - 4}{1}$ are:

The values of $p$ and $q$ such that the line joining the points $(7, p, 2)$ and $(q, -2, 5)$ is parallel to the line joining the points $(2, -3, 5)$ and $(-6, -15, 11)$ are:

The equation of a line passing through $(3, -1, 2)$ and perpendicular to the lines $\bar{r} = (\hat{i} + \hat{j} - \hat{k}) + \lambda(2\hat{i} - 2\hat{j} + \hat{k})$ and $\bar{r} = (2\hat{i} + \hat{j} - 3\hat{k}) + \mu(\hat{i} - 2\hat{j} + 2\hat{k})$ is:

The equation of the line equally inclined with the positive coordinate axes and passing through $(-3, 2, -5)$ is

The vector equation of the line $\frac{x+3}{2}=\frac{2y-3}{5}; z=-1$ is