Question

Determine whether the vectors u and v are parallel, orthogonal, or neither.

u = <3, 0>, v = <0, -6>

Answer 1

Orthogonal I believe

Answer 2

They are orthogonal.

Explanation:

u = <3, 0> v = <0, -6>

u.v =|u| |v|cosθ

if u.v is 0 this means that cos θ is 0 so θ = 90°

`\theta=cos^(-1)(u.v)/(|u|\ |v|)`

If u.v = 0 then they are orthogonal.

If u.v ≠ 0 then they are neither parallel nor orthogonal

If u.v ≠ 0 and u = kv where k is constant then they are parallel

u.v = 3×0+0×-6

⇒u.v = 0

They are orthogonal.