How Do You Solve for m and n to Make mA + nB + C Parallel to the Y-Axis?

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To determine values of m and n that make the vector mA + nB + C parallel to the y-axis, the x and z components of the resulting vector must equal zero while the y component remains non-zero. The expression for mA + nB + C is derived as (5m - n + 8)ax + (3m + 4n + 2)ay + (2m + 6n)az. Setting the x and z components to zero leads to the equations 5m - n + 8 = 0 and 2m + 6n = 0. The discussion clarifies that the vector must align with the direction <0, 1, 0>, confirming that the y component can be non-zero. The user expresses gratitude for the clarity, indicating they can now solve the problem.
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If A = 5ax + 3ay + 2az
B = -ax + 4ay + 6az
C = 8ax + 2ay

Find the value of m and n such that mA + nB + C is parallel to y-axis.

My problem is I did not know how to determine the m and n value because I did not know what method can use to solve for mA + nB + C parallel to y axis. Does it means that the vector line of mA + nB + C must be a straight line parallel to y axis?

mA + nB + C
= (5m - n + 8)ax + (3m + 4n + 2)ay + (2m + 6n)az

To use dot product means that (mA + nB + C) dot (??) = 1
cross product means that (mA + nB + C) cross (??) = 0

I don't know the ?? is stand for what... can someone pls help me?
 
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mA + nB + C should be a vector that should have same direction as <0,1,0>.

What that means is that other than y component not equals zero, x and z components should be zero.
 
Thanks, now I am able to solve the question :D
 

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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