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Planes

A plane has equation 2x +y -2z =7. The point q has coordinates 4,2,-3. Find the coordinates of P, the foot of the perpendicular from Q to the plane. I don’t understand what it’s asking for ?
Original post by avacados1
A plane has equation 2x +y -2z =7. The point q has coordinates 4,2,-3. Find the coordinates of P, the foot of the perpendicular from Q to the plane. I don’t understand what it’s asking for ?


Its asking you to determine where the normal through Q intersects the plane.
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avacados1
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Original post by RDKGames
Its asking you to determine where the normal through Q intersects the plane.


But how do I find the normal through q
Original post by avacados1
But how do I find the normal through q


Its a straight line with the same direction as the normal to the plane, and this line goes through Q.

So construct its equation and you got it.
(edited 4 years ago)
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avacados1
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Original post by RDKGames
Its a straight line with the same direction as the normal to the plane, and this line goes through Q.

So construct its equation and you got it.


So the equation of the line is ( 4,2,-3 ) + lambda( 3, 1,-2)? But I donno what to do next . Sorry for being annoying but my brains just fried today
Original post by avacados1
So the equation of the line is ( 4,2,-3 ) + lambda( 3, 1,-2)? But I donno what to do next . Sorry for being annoying but my brains just fried today


I suppose that 3 in the dir. vec is a typo.

So then this is the vector equation of the line in the form r=a+(lambda)b. You can get the plane equation in the form r.n=d. And sub in the r for the line into it just as you would in normal cartesian equations with y.

Then just solve for lambda and get your point.
Reply 6
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avacados1
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Original post by RDKGames
I suppose that 3 in the dir. vec is a typo.

So then this is the vector equation of the line in the form r=a+(lambda)b. You can get the plane equation in the form r.n=d. And sub in the r for the line into it just as you would in normal cartesian equations with y.

Then just solve for lambda and get your point.

Got the answer. Thanks a lot for the help🙂

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