Determine whether u and v are orthogonal, parallel, or neither. u =

v=

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