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# What will be the equation of a plane passing through the line of intersection(?) of two parallel planes, say x=5 and x=7?

290 Points
9 years ago

Hi Umesh,

Firstly the planes x=5 and x=7 will not intersct as they are parallel planes.

In case of other planes intersecting in a line, you can have infinite planes passing through the line of intersection.

Say P1=0 and P2=0 are two planes.

Then P1 + λP2 = 0, will be the family of planes passing through the line of intersection of P1 = 0, and P2 = 0.

Hope this helps.

Best Regards,

Umesh N
4 Points
9 years ago

Is it wrong to write x-5 + (lamda)(x-7) = 0? If so, what else does the equation mean?

290 Points
9 years ago

Hi Umesh,

It is not wrong to write it that way.

That will represent the family of planes that is paralled to the given two parallel planes.

Hope it helps.

Best Regards,