Let L 1 : 1 x − 1 = − 1 y − 2 = 2 z − 1 and L 2 : − 1 x + 1 = 2 y − 2 = 1 z be two lines. Let L 3 be a line passing through the point ( α , β , γ ) and be perpendicular to both L 1

Question

Let L 1 ​ : 1 x − 1 ​ = − 1 y − 2 ​ = 2 z − 1 ​ and L 2 ​ : − 1 x + 1 ​ = 2 y − 2 ​ = 1 z ​ be two lines. Let L 3 ​ be a line passing through the point ( α , β , γ ) and be perpendicular to both L 1 ​ and L 2 ​ . If L 3 ​ intersects L 1 ​ , then ∣5 α − 11 β − 8 γ ∣ equals :

TestHub · Accepted Answer

​ DR’s of L 3 ​ = m × n = ​ i ^ 1 − 1 ​ j ^ ​ − 1 2 ​ k ^ 2 1 ​ ​ = − 5 i ^ − 3 j ^ ​ + k ^ L 3 ​ : − 5 x − α ​ = − 3 y − β ​ = 1 z − γ ​ = λ A ( α − 5 λ , β − 3 λ , γ + λ ) L 1 ​ : 1 x − 1 ​ = − 1 y − 2 ​ = 2 z − 1 ​ = k ​ B ( k + 1 , − k + 2 , 2 k + 1 ) Now ​ α − 5 λ = k + 1 ⇒ α = 5 λ + k + 1 β − 3 λ = − k + 2 ⇒ β = 3 λ − k + 2 γ + λ = 2 k − 1 ⇒ γ = − λ + 2 k + 1 ∣5 α − 11 β − 8 γ ∣ = ∣ − 25∣ = 25 ​

Mathematics - 3D-Coordinate Geometry Question with Solution | TestHub

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