Question

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

Answer 1

Because u·v=0 they are orthogonal

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.