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

[Greychu]

If A = 5a_x + 3a_y + 2a_z
B = -a_x + 4a_y + 6a_z
C = 8a_x + 2a_y

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)a_x + (3m + 4n + 2)a_y + (2m + 6n)a_z

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?

 

[rootX]

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.

 

[Greychu]

Thanks, now I am able to solve the question :D