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Find the equation of plane $W: (Ax+By+Cz+D=0)$ that passes through point $M(-3,-1,0)$ and $N(0,1,2)$ and its normal to the plane $W_1: 2x-y+2z-1=0$.
I know that if two planes are normal then their vector are normal. So we can say that $AA_1+BB_1+CC_1=0$.
And I know how to find vector from $MN(x_2-x_1,y_2-y_1,z_2-z_1)$. I have no idea how to continue. Anyone can help please...

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Using the conditions of your problem we get the equations: $$-3A-B+D=0$$ $$B+2C+D=0$$ $$2A-B+2C=0$$

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HINT

  • from normal condition we obtain $2A-B+2C=0$

  • then use the also 2 condition of passage through points M and N to obtain other 2 equations

Note that we obtain a system of three equations in 4 unknowns but one among A,B,C,D can arbitrarily fixed.

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  • $\begingroup$ I get this equation 6x+10y-z+28=0. $\endgroup$ – Viktor Dimitrioski Apr 21 '18 at 13:35
  • $\begingroup$ @ViktorDimitrioski There is a probelm with N(0,1,2) which doesn't satisfy the equation. $\endgroup$ – user Apr 21 '18 at 13:58
  • $\begingroup$ @ViktorDimitrioski I've obtained $6x-2y-7z+16=0$ $\endgroup$ – user Apr 21 '18 at 14:02

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