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Find parametric equations of the plane that is parallel to the plane $3x+2y-z=1$ and passes through the point $(1,\,1,\,1)$.

My first thought was that since they were parallel, the two planes in question have the same normal vector, but I do not know how to continue. I hope that someone can give me a hint or point me in the right direction. Thanks.

Ice Tea
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Synchrowave
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    Have you found a parametric equation for the plane $3x+2y-z=1$? Or have you found a parametric equation for a plane before at all? – Servaes Nov 01 '18 at 17:11
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    I tried to. But I failed. I read the answers for https://math.stackexchange.com/questions/152467/parametric-form-of-a-plane but I just messed my brain up.. And I can't find anything in the book that explains it thouroghly. – Synchrowave Nov 01 '18 at 17:13
  • Are you familiar with the vector equation of a plane? – gen-ℤ ready to perish Nov 01 '18 at 17:13
  • Yes. It consists of a stationary vector and two vectors that are scaled by two coefficients. – Synchrowave Nov 01 '18 at 17:15
  • The equation parallel to the given equation is given by $$3x+2y-z+d=0$$ and now you must plug in $$x=1,y=1,z=1$$ to compute $d$ – Dr. Sonnhard Graubner Nov 01 '18 at 17:15
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    Oh, I ran across d a couple of times, and in my notes it is not even mentioned. So I must have somehow missed it. So it is basically a constant that determines the level of the plane? Or am I totally wrong here? – Synchrowave Nov 01 '18 at 17:17
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    No, you are right, then you can compute the parameter form – Dr. Sonnhard Graubner Nov 01 '18 at 17:18
  • Thanks a lot Doc. I computed the parameter form but it kinda feels like I had no idea what I just did.. So I have some follow up questions.. At the beginning of yesterdays lecture, my professor stated that a plane is determined by a point and two non-parallell vectors that are scaled by two variables. Then he procceds with stating that in the case of a scalar product resulting in 0, the two vectors are perpendicular to each other. Which derives the formula A(x-x0) + B(y-y0) +C(z-z0) + d = 0. While I understand the latter equation I don't understand how one can say that it represents the plane – Synchrowave Nov 01 '18 at 18:04
  • @Synchrowave If you’re having this much trouble understanding the material, you should really talk to your professor or a TA about it. – amd Nov 01 '18 at 19:11

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