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Question

Mathematics Question on Relations and functions

What is the acute angle between the lines represented by the equations y−3x−5=0 and 3y−x+6=0?

A

(A) 30∘

B

(B) 45∘

C

(C) 60∘

D

(D) 75∘

Answer

(A) 30∘

Explanation

Solution

Explanation:
Given,y−3x−5=03y−x+6=0y−3x−5=0⇒y=3x+5So, slope of line, m1=33y−x+6=0⇒y=x3−63So, slope of the line, m2=13Let θ be the acute angle between the lines.The angle θ between the lines having slope m1 and m2 is given by:tan⁡θ=|m1−m21+m1m2|⇒tan⁡θ=|3−131+3×13|⇒tan⁡θ=|232|⇒tan⁡θ=13⇒θ=30∘Hence, the correct option is (A).