The correct options are
A Coordinates of N are (5249,−7849,15649)
B Equation of line NQ is 3(x−3)=−(2y+9)=z−9
Since, N lies on line AB
and direction ratios of line AB is <2,−3,6>
So, coordinates of N≡(2r,−3r,6r)
(where r∈R be any constant)
∴ d.r.'s of PN is <2r−1,−3r−2,6r−5>
Since, PN⊥AB
∴2(2r−1)−3(−3r−2)+6(6r−5)=0⇒r=2649
So, N≡(5249,−7849,15649)
Now, let coordinates of Q be (2k,−3k,6k)
(where k∈R be any constant)
and d.r.'s of perpendicular of the given plane is <3,4,5>
Then d.r.'s of PQ is <2k−1,−3k−2,6k−5>
Since, PQ ∥ plane
∴3(2k−1)+4(−3r−2)+5(6k−5)=0⇒k=32
So, Q≡(3,−92,9)
∴ Equation of NQ is x−395=y+9/2−285/2=z−9285