Problem: The line x=1+t, y=1+2t, z=2-t is projected over the plane x-2y+3z-2=0, parallel with the vector a=(1,-1,0). Find the equation of the projected line. tnx
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Denote $\displaystyle \pi_1\equiv x-2y+3z=0$ and consider the plane $\displaystyle \pi_2\equiv (x,y,z)=(1,1,2)+\alpha (1,2,-1)+\beta (1,-1,0)$ The solution is $\displaystyle r\equiv \pi_1 \cap \pi_2$ Why?
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