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A plane π has vector equation $r =(-2 i+3 j -2 k )+λ(2 i +3 j+2 k )+μ(6 i-3 j +2 k)$. (a) Show that the Cartesian equation of the plane $\Pi$ is $3x+2y-6z=12$. (b) The plane $\Pi$ meets the x,y and z axes at $A, B$ and $C$ respectively. Find the coordinates of $A, B$ and $C$.

I used the Normal vector to solve the (a) part, but i don't know to find the coordinates of $A, B$ and $C$. If the plane meets the axis is it not intercession?

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Two methods:

  1. The $x$-axis, for instance, has equations $\; y=z=0$. So you only have to solve for $x$. Similarly for the other axes.
  2. Rewrite the equation in the form: $$\frac xa+\frac yb+\frac z c=1.$$ The intersections with the axes have coordinates $$(a,0,0),\quad (0,b,0),\quad (0,0,c).$$
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  • $\begingroup$ Oh thanks. I guess i didn't know the general form of breaking the Cartesian equation into Coordinates. Thanks man $\endgroup$ – Ashalley Samuel Aug 31 '17 at 14:39
  • $\begingroup$ A(4,0,0), B(0,6,0), C(0,0,-2) $\endgroup$ – Ashalley Samuel Aug 31 '17 at 14:41

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