Given equation of plane is x+y+z=5. The distance measured along the line x=y=z. Direction ratios of the given line is (1,1,1). So, the equation of line PQ is
x−1
1
=
y+5
1
=
z−9
1
=λ ⇒x=λ+1,y=λ−5,z=λ+9 lies on the plane x+y+z=5 ∴(λ+1)−(−λ+5)+(λ+9)=5 ⇒λ=−10 The coordinate of Q is (−9,−15,−1) and the coordinate of P is (1,−5,9) PQ=√(10)2+(10)2+(10)2=10√3 ∴2√3k=10√3⇒k=5