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

Create a free account to view solution

View Solution Free
Topic: Math miscellaneous·Practice all Math miscellaneous questions

More Math miscellaneous Questions

A person is to count 4500 currency notes. Let an denote the number of notes he counts in the nth minute. If a1 = a2 = .....In a right angle ᐃABC, ∠A = 90o and sides a, b, c are respectively, 5 cm, 4 cm and 3 cm. If a force F has mo...The number of values of k for which the linear equations 4x + ky + 2z = 0 ; kx + 4y + z = 0 ; 2x + 2y + z = 0 possess a ...Number of divisors of 1024 × (225)2 × (25)7 which are of the form 3k + 1 (where k is a whole number) is equal ...If (10)9 + 2(11)1 (10)8 + 3(11)2 (10)7+ ... + 10(11)9 = k(10)9, then k is equal to...