Question

find the angle between two lines root 3 X + Y is equal to 1 and X + root 3 Y is equal to 1​

Answer 1

Answer:

Angle between the two lines = 30°

Step-by-step explanation:

Writting the line equations in the format : - aX + bY + C = 0

1st line - √3X + Y = 1; can also be written as   -   √3X + Y - 1 = 0   .... (1)

2nd line - X + √3Y = 1; can also be written as  -  X + √3Y - 1 = 0  ....(2)

agle between the two lines in the formate aX+bY+c = 0, is given as

Tan θ = Ι (a1b2-b1a2)/(a1a2+b1b2) Ι

where a1,b1 and a2,b2 are  for 1st and 2nd line line.

∴ Tan θ = Ι (√3×√3-1×1)/(√3×1+1×√3) Ι

∴ Tan θ = Ι (3 - 1)/(2√3) Ι

∴ Tan θ = Ι (2)/(2√3) Ι

∴ Tan θ = (1 / √3)

But Tan 30° = (1/√3)

∴ θ = 30°

∴Angle between the two lines = 30°