Determine the vector and parametric equations

AI Thread Summary
The discussion focuses on determining the vector and parametric equations of a plane that includes the point C(1,-2,6) and the z-axis. It is established that any point on the z-axis, such as (0, 0, 1) and (1, -2, 5), lies within the plane. Additionally, it is noted that the point (0, 0, 0) is also part of the plane, although this information is not essential for solving the main problem. The conversation emphasizes understanding the implications of including the z-axis in defining the plane. Overall, the key takeaway is the identification of multiple points that confirm the plane's existence.
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Determine the vector and parametric equations of the plane that contains point C(1,-2,6) and the z-axis

I take this to mean that any point on the z-axis is valid so does that mean either (0, 0, 1) or (1, -2, 5) are also on the plane?
 
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You are right in saying that the points (0, 0, 1) and (1, -2, 5) are on the plane.

However, can you see that the point (0, 0, 0) is also on the plane? (You don't really need to know this to solve your question, but I thought it would be nice if you are aware of this fact) :wink:
 

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I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
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Thread 'Greatest possible value of a constant in polynomial'

Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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