Determine whether the vectors u and v are parallel, orthogonal, or neither. u = <10, 0>, v = <0, -9>

Answer:Orthogonal.Step-by-step explanation:Given:u = <10, 0>v = <0, -9>In unit vector notation, the above vectors can be re-written as:u = 10i + 0jv = 0i - 9jNow, note the following:(i) two vectors, u and v, are parallel to each other if one is a scalar multiple of the other. i.e u = kv or v = ku for some nonzero value of a scalar k.(ii) two vectors are orthogonal if their dot product gives zero. i.e u . v = 0Let's use the explanations above to determine whether the given vectors are parallel or orthogonal.(a) If parallelu = k v10i + 0j = k (0i - 9j)   ?When k = 1, the above equation becomes10i + 0j  ≠  0i - 9jWhen k = 2,10i + 0j ≠ 2(0i - 9j)10i + 0j ≠ 0i - 18jSince we cannot find any value of k for which u = kv or v = ku, then the two vectors are not parallel to each other.(b) If Orthogonalu.v = (10i + 0j) . (0i - 9j)   [multiply the i components together, and add the result to the multiplication of the j components]u.v = (10i * 0i) + (0j * 9j)u.v = (0) + (0)u.v = 0Since the dot product of the two vectors gave zero, then the two vectors are orthogonal.