The Cartesian equation of a line is $6x-2=3y+1=2z-2$. Then its vector from is:

If the lines $x = ay+b$, $z = cy+d$ and $x = py+q$, $z = ry+s$ are perpendicular, then $ap + cr$ is equal to

A line is perpendicular to two lines having direction ratios $1,-2,-2$ and $0,2,1$ then the direction cosines of the line are:

Match List-I with List-II

Choose the correct answer from the options given below:

The cartesian equation of a line is $x = ay+b$, $z = cy+d$. It's direction ratios are

Two points are moving along the lines :

$L_1: \vec{r} = (2\hat{i}+3\hat{j}+\hat{k}) + \lambda(\hat{i}+2\hat{j}+\hat{k})$

$L_2: \vec{r} = (\hat{i}+\hat{j}) + \mu(2\hat{i}+\hat{j}-\hat{k})$

where $\lambda$ and $\mu$ are real parameters , then which of the following statements are correct ?

A. The direction ratios of the line perpendicular to both lines are $<-1,1,-1>$.

B. The direction cosines of the second line $L_2$ are $<\dfrac{2}{\sqrt6},\dfrac{-1}{\sqrt6},\dfrac{-1}{\sqrt6}>$.

C. Angle between two lines is $\pi/3$.

D. The lines are skew lines.

Choose the correct answer from the options given below:

If two lines $\frac{x-3}{2} = \frac{y-4}{5} = \frac{z}{4}$ and $\frac{x-4}{3} = \frac{y-5}{6} = \frac{1-z}{k}$, are coplanar, then $k$ is equal to