The shortest distance between the lines $\frac{x+3}{1} = \frac{y-2}{2} = \frac{z+4}{3}$ and $\frac{x+3}{-3} = \frac{y+7}{2} = \frac{z-6}{4}$ is :

The foot of perpendicular from point $(2, 4, -1)$ on the line $\frac{x+5}{1} = \frac{y+3}{4} = \frac{z-6}{-9}$ is :

If a line makes angle $\pi/3$ and $\pi/4$ with the positive directions of x-axis and y-axis respectively, then the acute angle made by the line with positive direction of z-axis is

The direction ratios of the line $\frac{1-x}{3} = \frac{7y - 14}{2} = \frac{z-3}{2}$ are

The direction ratio's of line of intersection of two planes :

$2x + y + z + 47 = 0$ and $3x - 2y - z + 41 = 0$ are :

The equation of line passing through the points (2, -1, 3) and (4, 2, 1) is

(A) $\frac{x-2}{2} = \frac{y+1}{3} = \frac{z-3}{-2}$

(B) $\frac{x-4}{3} = \frac{y-2}{-2} = \frac{z-1}{2}$

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

(D) $\frac{x-4}{-2} = \frac{y-2}{-3} = \frac{z-1}{2}$

Choose the correct answer from the options given below:

If a line makes angles 90 degree, 60 degree and $\theta$ with $x, y$ and $z$ axis respectively, where $\theta$ is acute, then value of $\theta$ is: