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Problem 33 Hard Difficulty

Find an equation of the plane.

The plane through the points $ (2, 1, 2) , (3, -8, 6) $ and $ (-2, -3, 1) $


$$5 x-3 y-8 z=-9$$

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Video Transcript

Hello. The question is taken from victor's and geometry of the space. And The question is find the equation of the plane and the plane passing to the 3.2123 -86 and -2 -31. So let me right equation or plain passing to three points 212 3 -86 and 30s -2 -31 can be read Ernest. So let me write it days X -2 x -1 that minus two. And here three minus two minus eight minus 16 minus two and thirties minus two minus two minus three minus one and 1 -2 is equal to zero. So let me so always we get X -2 into they send this so we get- dining to minus when it's nine minus four into four minus 16. So here comes the plus sign plus 16 and the second one is minus by minus one into K -2 into 1 -2. So that will be -1 minus off -2 -2. It's -4 -4 in two plus 4 plus minus four Plus 4 16. So that will be plus 16. So plus that minus to win too -3 -1. That will be -4 into 1 -4 -9 in two -4. So that will be plus 36. Sofia we get -36 is equal to zero for those solving it. We get 25 x -50 minus y minus went into 15 Plus Zed -2 into -40 Is equal to zero. And further we get 25 weeks minus 50 -15. y plus 15 minus 40. 0 Plus 80 is equal to zero. And we get the value 25 weeks, okay -15 Y -4, visit 80 and 15 is 95 95 -50 45, so that will be 45 which is equal to zero. Taking five women, we get five weeks -3 Y ages eight plus nine is equal to zero. So the required answer for this question is five x minus three by- Exit is equal to -9 which is the required and some of discussion. Hope this clears your doubt and thank you.