Question

the measure of the acute angle between lines root 3 x minus y minus 2 is equal to zero and x minus root 3 Y + 1 is equal to zero is​

Answer 1

The given lines are

3

x+y=1 and x+

3

y=1

⇒y=−

3

x+1 and y=−

3

1

x+

3

1

Thus slope of line (1) is m

1

=−

3

while the s

1

The acute angle i.e;θ between the two lines is given by

tanθ=

∣

∣

∣

∣

∣

1+m

1

m

2

m

1

−m

2

∣

∣

∣

∣

∣

=

∣

∣

∣

∣

∣

∣

−

1+(−

3

)(−

3

1

)

3

+

3

1

∣

∣

∣

∣

∣

∣

=

∣

∣

∣

∣

∣

∣

1+1

3

−3+1

∣

∣

∣

∣

∣

∣

=

∣

∣

∣

∣

∣

2

3

−2

∣

∣

∣

∣

∣

⇒tanθ=

3

1

,θ=30

∘

Thus, the angle between the given lines is either 30

∘

or 180

∘

−30

∘

=150

∘