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Find an equation of the plane.

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

The scalar equation of the plane:

$2 x+y-z=8$

Vectors

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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.