Plane geometry problem

**patzer** · September 2nd 2011, 11:54 AM

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

Actually don't have any idea so I need your help.

**Siron** · September 2nd 2011, 12:53 PM

One given you can already use:
There's given the plane makes the angle $\frac{2\pi}{3}$ with the plane $\pi$ , in general the angle $\theta$ between two planes is given by the formula:
$\cos(\theta)=\frac{x_1\cdot x_2+y_1\cdot y_2+z_1\cdot z_2}{\sqrt{x_1^2+y_1^2+z_1^2}+\sqrt{x_2^2+y_2^2+z_ 2^2}}$

Where $(x_1,y_1,z_1)$ and $(x_2,y_2,z_2)$ are the coordinates of the normal vectors of the two planes.
You know the coordinates of the normal vector of the plane $\pi$ so you can use this given.

About the line $l$ I have to think about, but the line is given in a parametric presentation so maybe I would try to reform it to a cartesian presentation by for example the substitution, let $y=t$ . But I'm not sure about this.

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