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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
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B
2
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C
3
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D
2
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Solution

The correct option is C 3
Equation of the line is
x21=y+11=z21=rx=r+2,y=r1,z=r+2
The point (r+2,r1,r+2) lies on the plane 2x+y+z=9 is 2(r+2)+r1+r+2=9r=1
So, the coordinate of Q are (3,0,3) and thus
PQ=(32)2+(0+1)2+(32)2=3

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