The two vectors u and v are orthogonal if and only if u dot v = 0
Let's say we had these general vectors
u = ai + bj
v = ci + dj
The dot product based on those general vectors above, is
u dot v = a*c + b*d
notice the corresponding coordinates multiply together, then you add up the products
-----------------------------------------------------------------------------------------
In this particular problem,
u = ai+bj
u = -6i + 2j
so a = -6 and b = 2
Also,
v = ci + dj
v = -5i+8j
making c = -5 and d = 8
-----------------------------------------------------------------------------------------
Let's compute the dot product of u and v
u dot v = a*c + b*d
u dot v = -6*(-5) + 2*8
u dot v = 30 + 16
u dot v = 46
-----------------------------------------------------------------------------------------
The dot product result is NOT equal to zero. So the two vectors are NOT orthogonal.