Questions in 3-d

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The angle between the straight lines $\frac{x+1}{2}=\frac{y-2}{5}=\frac{z+3}{4}$ and $\frac{x-1}{1}=\frac{y+2}{2}=\frac{z-3}{-3}$ is
If direction ratios of two lines are $5,\,\,-12,\,13$ and $-3,\,4,\,5$ then the angle between them is
The shortest distance between the lines $\frac{x-3}{3}=\frac{y-8}{-1}=\frac{z-3}{1}$ and $\frac{x+3}{-3}=\frac{y+7}{2}=\frac{z-6}{4}$ is
If the direction ratios of two lines are given by $3lm-4\,ln+mn=0$ and $l+2m+3n=0$, then the angle between the lines is
Equation of x-axis is
The straight line $\frac{x-3}{3}=\frac{y-2}{1}=\frac{z-1}{0}$is
The angle between a line with direction ratios 2 : 2 : 1 and a line joining (3, 1, 4) to (7, 2, 12) is
The line $\frac{x-2}{1}=\frac{y-3}{1}=\frac{z-4}{-k}$ and $\frac{x-1}{k}=$ $\frac{y-4}{2}=\frac{z-5}{1}$ are coplanar, if
If direction cosines of two lines are proportional to (2, 3, –6) and (3, –4, 5), then the acute angle between them is
The equation to the straight line passing through the points (4, –5, –2) and (–1, 5, 3) is

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