Determine if vector u is orthogonal to vector v: u = – 6i + 2j and v = –5i + 8j .

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.