A line with positive direction cosines passes through the point P(2, – 1, 2) and makes equal angles with the coordinate axes. The line meets the plane 2x + y + z = 9 at point Q. The length of the line segment PQ equals

Answer

`sqrt3`

Explanation

The direction cosines of the line are `1//sqrt3, 1//sqrt3,,1//sqrt3`. Any point on the line at a distance `t` from `p(2, -1, 2)` is `(2+(t)/(sqrt3), -1+ (t)/(sqrt3), 2+ (t)/(sqrt3))`, which lies on
`2x+y+z-9=0`
`rArr" "t=sqrt3`