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Reflection of a Point about a Line

A line from o...

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A line from origin meets the line (x-2)/1 = (y-1)/-2 = (z+1)/1 and (x-8/3)/2 = ( y+3)/1 = (z-1)/1 at P and Q respectively. Find the distance PQ

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Q. A line from the origin meets the lines

\frac{x - 2}{1} = \frac{y - 1}{- 2} = \frac{z + 1}{1}

\frac{x - \frac{8}{3}}{2} = \frac{y + 3}{- 1} = \frac{z - 1}{1}

P

Q

respectively. If length

P Q = d

d^{2}

\frac{x + 1}{2} = \frac{y + 1}{3} = \frac{z + 1}{4}

meets the plane

x + 2 y + 3 z = 14

P

, then the distance between

P

and the origin is

Q. Find the shortest distance between the lines

\frac{x - 1}{1} = \frac{y + 1}{3} = z

\frac{x - 1}{3} = \frac{y - 2}{1}, z = 2

Q. A line with d.r's

(2, 7, - 5)

is drawn to intersect the lines

\frac{x - 5}{3} = \frac{y - 7}{- 1} = \frac{z + 2}{1}

\frac{x + 3}{- 3} = \frac{y - 3}{2} = \frac{z - 6}{4}

P

Q

respectively. Length of

P Q

Q. Equation of a plane which passes through the point of intersection of lines

\frac{x - 1}{3} = \frac{y - 2}{1} = \frac{z - 3}{2}

\frac{x - 3}{1} = \frac{y - 1}{2} = \frac{z - 2}{3}

and at greatest distance from the origin is

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