If shortest distance between the lines $\vec{r} = \hat{i} - \hat{j} + \lambda(2\hat{i}+\hat{k})$ and

$\vec{r} = 2\hat{i} - \hat{j} + \mu(\hat{i}-\hat{j}-\hat{k})$ is $\dfrac{\sqrt{14}}{14}m$ units, the value of $m$ is

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

The foot of perpendicular from the point P (1, 2, -3) to the line $\frac{x+1}{2} = \frac{y-3}{-2} = \frac{z}{-1}$ is

The co-ordinates of the point at which the line $\frac{x-3}{3} = \frac{y+1}{2} = \frac{z-4}{-2}$ crosses x-y plane, are

If the points $A(-1,3,2)$, $B(-4,2,-2)$ and $C(5,5,\lambda)$ are collinear, then value of $\lambda$ is :

If the lines $\frac{1-x}{3} = \frac{y-2}{2\lambda} = \frac{z-3}{2}$ and $\frac{x-1}{3\lambda} = \frac{y-1}{1} = \frac{6-z}{5}$ are perpendicular, then $\lambda$ is equal to

For a given line L: $\dfrac{x}{2}=\dfrac{y+1}{3}=\dfrac{-z-3}{-5}$, which of the following is/are True ?

(A) The direction ratio of line L is (2, 3, -5)

(B) The perpendicular distance of the point (1, 1, 3) on the line L is $\sqrt{3}$

(C) The foot of perpendicular from the point (1, 1, 3) on line L is (2, 2, 1)

(D) The image of point (1, 1, 3) with respect to line L is (3, 3, 1)

Choose the correct answer from the options given below: