Originally Posted by
Siron This is the way I would do it:
Given a plane $\displaystyle \alpha$ and two points $\displaystyle P_1 (2,2,-1) ,P_2 (3,4,2) \in \alpha $ and the plane is parallel to a line who's direction ratios are $\displaystyle (7,0,6)$. In general the vector equation of a plane through one point $\displaystyle P_1$ and with two directions vectors $\displaystyle R,L$is: $\displaystyle P=P_1+kR+mL$. Now we already have (we work now in a three dimensional space):$\displaystyle (x,y,z)=(2,2,-1)+k(7,0,6)+mL$. Can you determine the other direction vector $\displaystyle L$?
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