If the two lines given by

$x=py+q, z=ry+s$ and

$x=p'y+q', z=r'y+s'$

are perpendicular, then which of the following is equal to -1 ?

The angle between the pair of lines given by $\vec{r} = \hat{i} + 2\hat{j} - 3\hat{k} + \lambda (\hat{i} - 2\hat{j} + 2\hat{k})$ and $\vec{r} = 5\hat{i} + \hat{j} + \hat{k} + \mu (3\hat{i} - 2\hat{j} + 6\hat{k})$ is

Given a line $L:\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}$, then

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The shortest distance between the lines whose vector equations are $\vec{r} = (6\hat{i}+2\hat{j}+2\hat{k}) + \lambda(\hat{i}-2\hat{j}+2\hat{k})$ and $\vec{r} = (-4\hat{i}-\hat{k}) + \mu(3\hat{i}-2\hat{j}-2\hat{k})$

The angle between the line $2x = 3y = z$ and $x$- axis is:

Equation of y-axis in space, in vector form is :

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