(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider P(2,1,3) and the line L: [tex]\begin{Bmatrix}x-y-5=0 \\z-1=0 \end{matrix}[/tex]

a) Find the equation of the line that pass through P and cuts L on a perpendicular angle.

b)Finds the points A and B in L in a way that PAB being an equilateral triangle.

2. Relevant equations

I've solved A, and I'm trying to solve b. I think that it can't be much difficult, cause I know all of the interior angles of PAB. I have a trigonometric problem. I've calculated the distance from L to P, so I got the high of the triangle. So, I know that [tex]sin 60º=h[/tex], I got [tex]h=\sqrt[ ]{22}[/tex], so what I know is that [tex]sin 60º=\sqrt[ ]{22}[/tex], so the cosine would be the half of the base. How should I get the base?

3. The attempt at a solution

I've found L2: [tex]\begin{Bmatrix}x=2+5\mu \\y=1+7\mu \\z=3+4\mu \end{matrix}[/tex]. So, I need to find the points A and B on L.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Trigonometry - Finding equation of line

**Physics Forums | Science Articles, Homework Help, Discussion**