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A line with positive direction cosines p...

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

A

1

B

`sqrt(2)`

C

`sqrt(3)`

D

2

Text Solution

Verified by Experts

The correct Answer is:
C
Since, `l=m=n=(1)/(sqrt(3))`

`:."Equations of line are "(x-2)/(1//sqrt(3))=(y+1)/(1//sqrt(3))=(z-2)/(1//sqrt(3))`
`implies" "x-2=y+1=z-2=r" "["say"]`
`:.`Any point on the line is
`Q-=(r+2,r-1,r+2)`
`because`Q lies on the plane `2x+y+z=9`
`:." "2(r+2)+(r-1)+(r+2)=9`
`implies" "4r+5=9impliesr=1`
`implies" "Q(3,0,3)`
`:.PQ=sqrt((3-2)^(2)+(0+1)^(2)+(3-2)^(2))=sqrt(3)`
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