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Problem 34 Medium Difficulty

Find an equation of the plane.

The plane through the points $ (3, 0, -1) , (-2, -2, 3) $ and $ (7, 1, -4) $

Answer

$2 x+y+3 z=3$

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Video Transcript

Hello. So the question is taken from victor's in geometry of the space. And we have to find the equation of plane. The plane passing to the 0.30 minus one minus two minus 23 and seven? One minus four. So let me write that equation of plane mm passing to Please U -1 -1 -2 -23. And 3rd point is 7. -4 can be read Ernest mode X -3 x zero. And that plus one. That is that minus of -1. So we get that plus one. Ex not X but minus two minus three. So yes minus two minus three minus two minus zero. And then three minus of minus one is plus one. Okay and third minus seven minus three 1 0 and 30 -4. mine minus four minus of minus one is minus four plus one. So let me further solve it in order to make it smaller wicket x minus three. Yeah we get -54. Why minus two 10 Plus one. Four minus three is equal to zero. Now using the coast multiplication we get x minus three basically the process of solving their determinant 6 -4- or Y -5-plus 8 Plus is a plus one Into -5-plus 8 checking minus So for why it will be my 15 -16 solely for that. When we take why we have to choose -544 and -3. So that will be -4 -3 is 15. And that will be for my four into 40 16. for minus 16 is equal to zero. Yeah. Yeah. Mhm mm hmm. two into X -3 plus why? Plus 303 in Tuesday plus one which is equal to 0, 15 minus 16 is minus went into minus one plus one. So that will be plus Y 2, -6 plus Y plus trees. It Plus three is equal to zero and eventually we get really equal to two, x plus y plus trees. It is equal to three which is the required equation of plane passing to the given points. So hope this closure doubt and thank