Answer:
Orthogonal.
Explanation:
Given:
u = <10, 0>
v = <0, -9>
In unit vector notation, the above vectors can be re-written as:
u = 10i + 0j
v = 0i - 9j
Now, 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 = 0
Let's use the explanations above to determine whether the given vectors are parallel or orthogonal.
(a) If parallel
u = k v
10i + 0j = k (0i - 9j) ?
When k = 1, the above equation becomes
10i + 0j ≠ 0i - 9j
When k = 2,
10i + 0j ≠ 2(0i - 9j)
10i + 0j ≠ 0i - 18j
Since 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 Orthogonal
u.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 = 0
Since the dot product of the two vectors gave zero, then the two vectors are orthogonal.