Question

determine u and v are orthogonal, parallel, or neither. u=(15, 45) v=(-5, 12)

Answer 1

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

Answer 2

thanks very much, just wanted to make sure it was neither

Answer 3

your welcome

Answer 4

To see that they are not parallel, notice that u is not equal a scalar v
if
u=(15, 45) v=(-5, 12)
\[
u= a ( v)\\
15 = - 5 a \\
45 = 12 a \\

a= -3\\
a =\frac { 45}{12}\ne -3
\]