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Problem 24 Easy Difficulty

Find an equation of the plane.

The plane through the point $ (5, 3, 5) $ and with normal vector $ 2i + j - k $

Answer

The scalar equation of the plane:
$2 x+y-z=8$

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Video Transcript

Hello. So the ocean is taken from vectors and geometry of the space. And we have to find an equation of plane. The plane passes to 535. And with normal vector two Y plus J minus K. So that point by which the plane passes to five 3 5. and normal victories two I close g minus. Okay so let me right. The equation of clean passes to that is this is victor passes two five, 35 and mhm. No money uh vectors E can be mm Oh you don't ask vector A dot X minus five into I plus Why -3 into J plus zero minus five and two K. Which is the required form of the situation. Okay Since the two electoral perpendicular so therefore there will be zero and vector A given S two y plus J -K. Doored X -5 into I Plus Y -3 into J Plus Save -5 went okay okay. Using the property of those products do I daughter is too so that would be too into x minus five Plus Y -3 minus scared. Or this that will be minus zero minus five is equal to zero. On solving it we get two weeks plus y minus z minus 10 minus three plus five is equal to zero. And for those solving it we get equation of plane is two weeks plus y minus that is minus 13 plus five with eight. So which is the required equation of plane that passes to +535. And normal to the plane normal to the victor to white, J minus K. Hope this clears your doubt and thank you.