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

Find the equation of plane which contains the line [itex]l:\left\{\begin{array}{l} x=t+2 \\y=2t-1\\z=3t+3 \end{array}\right.[/itex], and makes the angle of [itex]\frac{2\pi}{3}[/itex] with the plane [itex]\pi:x+3y-z+8=0[/itex].

3. The attempt at a solution

My attempt was to find the normal vector of plane which contains the line by the cross product of vector [itex]\vec{a}[/itex] of line and some vector created between points [itex]P(2,-1,3)[/itex] of line and point [itex]Q(x,y,z)[/itex], than by using the formula to find angles, but this leads me to complications.

I think there's another way to solve this, which I don't know.

Thank you

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# Plane geometry problem

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