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Question

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

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Solution

The given lines are 3x+y=1 and x+3y=1
y=3x+1 and y=13x+13
Thus slope of line (1) is m1=3 while the slope of line (2) is m2=13
The acute angle i.e;θ between the two lines is given by
tanθ=m1m21+m1m2
=∣ ∣ ∣3+131+(3)(13)∣ ∣ ∣
=∣ ∣ ∣3+131+1∣ ∣ ∣=223
tanθ=13,θ=30
Thus, the angle between the given lines is either 30 or 18030=150

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