2. Prove that the vectors are orthogonal unit vectors for any value of 0 u = (coso,-sino), v = (sino, cos)

Because u·v=0 they are orthogonal

Step-by-step explanation:

Let's find the solution by using the dot product, taking into account that two vectors are orthogonal if its dot product is equal to 0, so:

u = (cos (o),-sin (o))

v = (sin (o), cos (o))

Let's find the dot product:

u·v = (cos (o),-sin (o)) * (sin (o), cos (o))

u·v=cos (o) * sin (o) + (-sin (o) * cos (o))

u·v=cos (o) * sin (o) - sin (o) * cos (o)

u·v=0

In conclusion, for any value of o, u·v=0. So u and v are orthogonal.