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Question

Find the angles between the lines 3x+uy=1 and x+3y=1

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Solution

Let the slopes of the given lines be m1 and m2 respectively.

Now, 3x+y=1y=3x+1

and x+3y=1y=13x+13

m1=3m2=13

tanθ = m2m11+m1m2 = ∣ ∣13+3{1+(3)×(13)}∣ ∣

= 23×12 = 13

= 13 θ=30(180θ)=(18030)=150.

Hence, the angles between the given lines are 30 and 150


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