Math miscellaneousHard

Question

Let P be the point (1,2,3) and Q be a point on the line . Then the
value of λ for which line PQ is perpendicular to the plane 4x + 9y - 18z = 1 is-

Options

A.1/3
B.-1/6
C.-2/3
D.2/5

Solution

       
Any point on line is Q(1 - 2λ, - 1 + 3λ, 5 + 4λ)
∴  Direction ratios of PQ
are (-2λ, 3λ -3, 4λ + 2)
PQ is perpendicular to the plane
⇒  PQ is parallel to normal of the plane
⇒ 
⇒  λ = 2/5

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