Question

Determine whether 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