Question

Derive a formula to find the angle between two lines with slopes m1 and my. Hence find the angle between the lines y= √3x+5 and y = 1/√3x-2√3
​

Answer 1

Answer:

L

1

:

3

x+y=1;L

2

:x+

3

y=1

m

1

=−

3

;m

2

=

3

1

tanθ=

∣

∣

∣

∣

∣

1+m

1

m

2

m

1

−m

2

∣

∣

∣

∣

∣

=

∣

∣

∣

∣

∣

∣

∣

∣

∣

1+(−

3

)(

3

−1

)

−

3

−

3

1

∣

∣

∣

∣

∣

∣

∣

∣

∣

=

∣

∣

∣

∣

∣

∣

∣

∣

∣

1+1

3

−3−1

∣

∣

∣

∣

∣

∣

∣

∣

∣

=

1

2

3

−4

=

3

−2

∴tanθ=

3

−2

∴θ=tan

−1

(

3

−2

).