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Question

Find the acute angle between the lines 3x+y=1 and x+3y=1.

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Solution

L1:3x+y=1;L2:x+3y=1

m1=3;m2=13

tanθ=m1m21+m1m2

=∣ ∣ ∣ ∣ ∣3131+(3)(13)∣ ∣ ∣ ∣ ∣

=∣ ∣ ∣ ∣3131+1∣ ∣ ∣ ∣

=4321

=23

tanθ=23

θ=tan1(23).

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