Question

the equation of the line through the origin making an angle of 60 degree with the line X + Y root 3 + 3 root 3 is equal to zero

Answer 1

Answer:

x - √3 y = 0  ( 60° anticlockwise )

If you also need 60° clockwise, then also the line

x = 0  (i.e. the y-axis)

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Step-by-step explanation:

Let θ be the angle that the line

x + √3 y + 3√3 = 0

makes with the x-axis ( -90° < θ ≤ 90° )

Then tan θ = - 1 / √3  =>  θ = -30°.

That is, the line goes down at an angle 30° from the x-axis.

A line that makes an angle of 60° (measured anticlockwise) with this line is then going to make an angle of

θ + 60° = -30° + 60° = 30°

with the x-axis.

tan 30° = 1 / √3  =>  equation is x - √3 y + c = 0.

line goes through the origin => c = 0

So the equation of the line is

x - √3 y = 0

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If we also want the line that makes an angle 60° measured clockwise, then the new line will make an angle of θ - 60° = -30 - 60° = -90° with the x-axis.  As the line passes through the origin, it is the y-axis.  Equation is then:

x = 0