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im really confuse how to figure this one out... Can someone please help me

Parcly Taxel
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Pyun - pyun
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  • Two planes are parallel if (and only if) they don't meet, so if (and only if) the two equations have no common solution. So, you know how to find solutions of two linear equations in three unknowns? – Gerry Myerson Apr 14 '20 at 06:40
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    A plane with equation $ax+by+cz=d$ has normal vector $(a,b,c)$. Two planes are parallel if their normal vectors are proportional. With these indications, work this issue by yourself ! – Jean Marie Apr 14 '20 at 06:41
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    Welcome to MSE. It is in your best interest that you type your questions (using MathJax) instead of posting links to pictures. – José Carlos Santos Apr 14 '20 at 06:43
  • @GerryMyerson Planes can meet and be parallel (i.e. coincident planes: they are scalar multiples of each other). – Andrew Chin Apr 14 '20 at 07:10
  • @Andrew I wouldn't call planes (or lines) parallel, if they are coincident. Do you have a cite for this definition? – Gerry Myerson Apr 14 '20 at 12:01
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    @GerryMyerson Did some digging and found a discussion. I choose to accept that coincident lines are parallel lines that maintain a distance of zero from each other (but I'm not sure I want to get into the argument of what "distance" is lol) – Andrew Chin Apr 14 '20 at 17:56

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Hints: Let ${\bf n_i}$ be the normal of plane $i=1,2,3,4$. Notice that

\begin{align*} {\bf n_1} &= (15, -6, 24) \\ {\bf n_2} &= (-5,2,-8) \\ {\bf n_3} &= (6,-4,4) \\ {\bf n_4} &= (3,-2,-2) \\ \end{align*}

What happens when the normals of two planes are parallel?

James
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