Let Q be the point where the line through P(1,−5,9) and parallel to r=
^
i
+
^
j
+
^
k
meets the plane r(
^
i
−
^
j
+
^
k
)=5 Equation of PQ, is
x−1
1
=
y+5
1
=
z−9
1
=λ ∴ x=λ+1 y=λ−5 andz=λ+9 lies on the plane x−y+z=5 ⇒λ+1−λ+5+λ+9=5 ⇒λ=−10 ∴ Co-ordinates of Q are Q(−9,−15,−1) ⇒PQ=√102+102+102=10√3