plane perpendicular to the planes 2x-y+z-3=0 and -x+3z-2=0

[Max12345]

Find the plane perpendicular to the planes and . Check, ifknowing only this we can find exactly one answer. If not, add anycondition to get just one plane .

 

[tkhunny]

Find the plane perpendicular to the planes and . Check, ifknowing only this we can find exactly one answer. If not, add anycondition to get just one plane .

Perhaps you could share your planes with us - and your best work toward a solution?

What do we know about Dot Products and Perpendiculars?

 

[Dr.Peterson]

Find the plane perpendicular to the planes and . Check, ifknowing only this we can find exactly one answer. If not, add anycondition to get just one plane .

It looks like you pasted from a source that was not all text. Always proofread!

Please type the whole problem out, including any context we need to know, and tell us your own thinking.

 

[Max12345]

Sorry
Find the plane perpendicular to the planes 2x-y+z-3=0 and -x+3z-2=0 . Check, ifknowing only this we can find exactly one answer. If not, add anycondition to get just one plane .

 

[pka]

Find the plane perpendicular to the planes 2x-y+z-3=0 and x-3z+2=0 . Check, ifknowing only this we can find exactly one answer. If not, add anycondition to get just one plane .

I confess confusion about this question. It is posted in a geometry-trig sub-forum but requires vector geometric methods to solve (see tkhunny's reply). The planes have normals \(\displaystyle \left\langle {2, - 1,1} \right\rangle ~\&~ \left\langle {1,0, - 3} \right\rangle \) so that \(\displaystyle \left\langle {2, - 1,1} \right\rangle \times \left\langle {1,0, - 3} \right\rangle = \left\langle {3,7,1} \right\rangle \). By inspection we see that the point \(\displaystyle (1,0,1)\) belongs to both planes. So the line \(\displaystyle \ell(t)=<1,0,1>+t<3,7,1>\) is the line of intersection of the two planes. Now any plane with normal \(\displaystyle <3,7,1>\) will be perpendicular to the given planes. Thus if we require that the plane contains the point \(\displaystyle (1,0,1)\) the answer will be unique.