The shortest distances of the point $(1, 2, 3)$ from $x$, $y$, $z$ axes respectively are

Consider the line $\frac{x-2}{2} = \frac{2y-5}{-3}, z = -1$. Then which of the following is/are true?

(A) It has Direction ratios (2, -3, -1)

(B) It has Direction cosines $\left(\frac{4}{5}, \frac{-3}{5}, \frac{-1}{5}\right)$

(C) It has Direction ratios $\left(2, \frac{-3}{2}, 0\right)$

(D) It has Direction cosines $\left(\frac{4}{5}, \frac{-3}{5}, 0\right)$

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Distance between the point (3, 4, 5) and the point where the line $\frac{x-3}{1} = \frac{y-4}{2} = \frac{z-5}{2}$ meets the plane $x + y + z = 17$ is :

The foot of perpendicular from the point P (1, 2, -3) to the line $\frac{x+1}{2} = \frac{y-3}{-2} = \frac{z}{-1}$ is

Consider two lines $l_1$ and $l_2$ with cartesian equations $\frac{x}{2} = \frac{1-y}{-2} = \frac{z}{1}$ and $\frac{2x-5}{16} = \frac{y-2}{-1} = \frac{z-5}{4}$ respectively. Which of the following is/are true?

(A) Direction ratio of $l_1$ are 2, 2, 1

(B) Direction cosines of $l_1$ are $\frac{2}{3}, \frac{-2}{3}, \frac{1}{3}$

(C) Direction ratio of $l_2$ are 16, -1, 4

(D) Angle between $l_1$ and $l_2$ is $\cos^{-1}\left(\frac{38}{3\sqrt{273}}\right)$

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The angle between 2 planes $4x + 8y + z - 8 = 0$ and $y + z - 4 = 0$ is :

The vector equation of line passing through $(-1, 3, -2)$ and perpendicular to the lines $\frac{x+4}{1} = \frac{y}{2} = \frac{z-3}{3}$ and $\frac{x+2}{-3} = \frac{y+5}{2} = \frac{z-6}{5}$ is