I want to find for which values of M vectors$A(m-4,2,2m-12),B(2,m-12,2)$ are orthogonal.
what I did is to do $A*B=0$ and the result was $m=7$ then I inserted $7$ and tried to check if they are orthogonal but it didnt gave me $0.$
there is something wrong with the way I did it?
Thanks!
my calculations:
$A*B = 2m-8+2m-24+4m-24=0 \rightarrow 8m=56 \rightarrow m=7$
$$ A \cdot B = 2(m-4) + 2(m-12) + 2(2m-12) = 2m - 8 + 2m - 24 + 4m - 24 = 8m - 56 = 0 $$ from which you can find that $m = 7$ is indeed a solution. To check it just substitute it back $$ A \cdot B = (3, 2, 2) \cdot (2, -5, 2) = 6 - 10 + 4 = 0 $$