Chapter 22

The distance of the point \((1,0,2)\) from the point of intersection of the line \(\frac{x-2}{3}=\frac{y+1}{4}=\frac{z-2}{12}\) and the plane \(x-y+z=16\), is: (A) 8 (B) \(3 \sqrt{21}\) (C) 13 (D) \(2 \sqrt{14}\)

The equation of the plane containing the lines \(2 x-5 y\) \(+z=3\) and \(x+y+4 z=5\), and parallel to the plane, \(x+\) \(3 y+6 z=1\), is: \([\mathbf{2 0 1 5}]\) (A) \(x+3 y+6 z=-7\) (B) \(x+3 y+6 z=7\) (C) \(2 x+6 y+12 z=-13\) (D) \(2 x+6 y+12 z=13\)

The distance of the point \((1,-5,9)\) from the plane \(x-y\) \(+z=5\) measured along the line \(x=y=z\) is: \(\quad\) [2016](A) \(\frac{20}{3}\) (B) \(3 \sqrt{10}\) (C) \(10 \sqrt{3}\) (D) \(\frac{10}{\sqrt{3}} \mid\)