If the two lines $x = ay + b, z = cy + d$ and $x = a'y + b', z = c'y + d'$ are perpendicular,then which of the following is true?

If lines $\frac{2x-4}{\lambda}=\frac{y-1}{2}=\frac{z-3}{1}$ and $\frac{x-1}{1}=\frac{3y-1}{\lambda}=\frac{z-2}{1}$ are perpendicular to each other,then $\lambda = \ldots$.

The equations of motion of a rocket are: $x = 2t, y = -4t, z = 4t$ where the time $t$ is given in seconds,and the coordinates of a moving point in kilometers. What is the path of the rocket? At what distance will the rocket be from the starting point $O(0, 0, 0)$ in $10$ seconds?

Let $A$ and $B$ be two points on the line $\frac{x}{1} = \frac{y}{1} = \frac{z}{-1}$. If the distance of point $P(1, 1, 1)$ from the points $A$ and $B$ is $\sqrt{3}$,then the distance between $A$ and $B$ is:

Consider the line $L$ passing through the points $(1, 2, 3)$ and $(2, 3, 5)$. The distance of the point $A\left(\frac{11}{3}, \frac{11}{3}, \frac{19}{3}\right)$ from the line $L$ along the line $\frac{3x-11}{2} = \frac{3y-11}{1} = \frac{3z-19}{2}$ is equal to:

The point collinear with $(1, -2, -3)$ and $(2, 0, 0)$ among the following is