Verify that lines given by $\vec{r}=(1-\lambda)\hat{i}+(\lambda-2)\hat{j}+(3-2\lambda)\hat{k}$ and $\vec{r}=(\mu+1)\hat{i}+(2\mu-1)\hat{j}-(2\mu+1)\hat{k}$ are skew lines. Hence, find shortest distance between the lines.

If points $(2, 3)$, $(0, 4)$ and $(p, 2)$ are collinear, then the value of p is:

Find the angle between the following pair of lines: $\frac{x-2}{3}=\frac{y+5}{2}=\frac{1-z}{-6}$ and $\frac{x-7}{1}=\frac{y}{2}=\frac{6-z}{-2}$.

If $l_{1}$, $m_{1}$, $n_{1}$ and $l_{2}$, $m_{2}$, $n_{2}$ are direction cosines of lines $L_{1}$ and $L_{2}$ respectively and $\theta$ is the acute angle between them, then :

Position vectors of the points A, B and C as shown in the figure below are a, $\vec{b}$ and $\vec{c}$ respectively. If $\vec{AC}=\frac{5}{4}\vec{AB}$ , express $\vec{c}$ in terms of $\vec{a}$ and $\vec{b}$ . OR Check whether the lines given by equations $x=2\lambda+2$, $y=7\lambda+1$, $z=-3\lambda-3$ and $x=-\mu-2,$ $y=2\mu+8,$ $z=4\mu+5$ are perpendicular to each other or not.