NTA Abhyas JEE Main2020MathematicsThree Dimensional GeometryPractice

If the line x - 1 1 = y - k - 2 = z - 3 λ lies in the plane 3 x + 4 y - 2 z = 6, then 5 k + 3 λ is equal to

Options

A75
B75 4
C15
D5 2

Correct answer

B. 75 4

Step-by-step solution

If the line x - 1 1 = y - k - 2 = z - 3 λ lies in the plane 3 x + 4 y - 2 z = 6 ⇒ 1 , k , 3 satisfies the equation of the plane ⇒ 3 + 4 k - 6 = 6 ⇒ k = 9 4 And b → ⋅ n → = 0 b → = 1 , − 2 , λ and n → = 3 , 4 , − 2 ⇒ 3 - 8 - 2 λ = 0 ⇒ λ = - 5 2 5 k + 3 λ = 45 4 + 15 2 = 75 4

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