Determine whether u and v are orthogonal, parallel, or neither. u = < 15,45>
v= < -5,12>

Take the dot product, if the dot product is zero, they are orthogonal 

the dot product here is 15(-5) + 45(12) so the vectors are not orthogonal 

to see if they are parallel, take the dot product again, using the definition 

u dot v = mag u x mag v cos (theta) where mag is the magnitude of the vector and theta is the angle between them 

we know from above that u dot v = 465 

mag u = sqrt[15^2+45^2]=47.43 
mag v = sqrt[5^2+12^2]=13 

so we know: 

cos(theta) = 465/(47.43x13) = 0.75 

so theta = 41 deg