Let θ 1 be the angle between two lines 2 x + 3 y + c 1 = 0 and − x + 5 y + c 2 = 0 and θ 2 be the angle between two lines 2 x + 3 y + c 1 = 0 and − x + 5 y + c 3 = 0 , where c 1 , c 2

Question

Let θ 1 ​ be the angle between two lines 2 x + 3 y + c 1 ​ = 0 and − x + 5 y + c 2 ​ = 0 and θ 2 ​ be the angle between two lines 2 x + 3 y + c 1 ​ = 0 and − x + 5 y + c 3 ​ = 0 , where c 1 ​ , c 2 ​ , c 3 ​ are any real numbers : Statement-1: If c 2 ​ and c 3 ​ are proportional, then θ 1 ​ = θ 2 ​ . Statement-2: θ 1 ​ = θ 2 ​ for all c 2 ​ and c 3 ​ .

TestHub · Accepted Answer

Two lines − x + 5 y + c 2 ​ = 0 and − x + 5 y + c 3 ​ = 0 are parallel to each other. Hence statement-1 is true, statement-2 is true and statement-2 is the correct explanation of statement-1.

Mathematics - Straight Lines Question with Solution | TestHub

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