Since direction cosines of PQ are equal and positive. ∴ The d.r.s. of PQ are
1
√3
,
1
√3
,
1
√3
∴ The equation of the line PQ is
x−2
1
√3
=
y+1
1
√3
=
z−2
1
√3
⇒x−2=y+1=z−2=k, say ∴ Co-ordinates of the point Q are (k+2,k−1,k+2) The point Q lies on the plane x+y+z=9 ∴2(k+2)+k−1+k+2=9 ⇒4k+5=9⇒k=1 ∴Q≡(3,0,3) ∴PQ=√(3−2)2+(0+1)2+(3−2)2 =√1+1+1=√3