Vector Algebra & Analytcc geometry in space

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The discussion focuses on finding resources such as video tutorials or e-books for vector algebra and analytic geometry in space. A user seeks assistance in determining the intersection point of two vectors given their initial points and equations. The conversation emphasizes the need for clear instructional materials to understand these concepts. Participants are encouraged to share useful links or recommendations. Understanding how to calculate intersection points is a key topic of interest.
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Please can somebody help me to find video tutorials or e-books for these
 
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if we have the initial point of two vectors and equations of these vectors , how can we find the intersection point of these vectors
 
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
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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