Questions in 3-d

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The length of the perpendicular drawn from the point (5, 4, –1) on the line $\frac{x-1}{2}=\frac{y}{9}=\frac{z}{5}$ is
The length of the perpendicular from point (1, 2, 3) to the line $\frac{x-6}{3}=\frac{y-7}{2}=\frac{z-7}{-2}$is
The angle between the lines whose direction cosines are connected by the relations $l+m+n=0$ and $2lm+2nl-mn=0$, is
The perpendicular distance of the point (2, 4, –1) from the line $\frac{x+5}{1}=\frac{y+3}{4}=\frac{z-6}{-9}$ is
The angle between two lines $\frac{x+1}{2}=\frac{y+3}{2}=\frac{z-4}{-1}$ and $\frac{x-4}{1}=\frac{y+4}{2}=\frac{z+1}{2}$ is
The straight lines $\frac{x-1}{1}=\frac{y-2}{2}=\frac{z-3}{3}$ and $\frac{x-1}{2}=\frac{y-2}{2}=\frac{z-3}{-2}$ are
The equation of the line passing through the points ( 3, 2, 4) and (4, 5, 2) is
The angle between the lines $\frac{x+4}{1}=\frac{y-3}{2}=\frac{z+2}{3}$ and $\frac{x}{3}=\frac{y-1}{-2}=\frac{z}{1}$ is
The angle between the pair of lines with direction ratios (1, 1, 2) and $(\sqrt{3}-1,-\sqrt{3}-1,4)$ is
The acute angle between the line joining the points (2,1,–3), (–3,1,7) and a line parallel to $\frac{x-1}{3}=$ $\frac{y}{4}=\frac{z+3}{5}$ through the point (–1, 0, 4) is

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