Question

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

u = <1, -2>, v = <-4, 8>

Answer 1

take their dot product

Answer 2

Let
U = (u1,u2)
V= (v1,v2)

Dot product is
U.V = u1 * v1 + u2*v2

Answer 3

you also can generalize this
Given
U = (u1,u2,...,un)
V= (v1,v2,...,vn)

Dot product is defined as
U.V = u1 * v1 + u2*v2 + ... un*vn

Answer 4

now there are also some geometric facts

since
U . V = | U |*|V|*cos (theta) , where theta is between vectors U, V

Answer 5

if theta is 90 degrees between the vectors, cos theta = 0, so we have
U. V = 0 , when theta is 90 degrees

Answer 6

if the angle between them is 180 degrees or 0 degrees, then U and V are parallel .
and cos(180) = -1

but its easier to see if two vectors are parallel
U is parallel to V when U = k*V

Answer 7

u = <1, -2>, v = <-4, 8>

i notice that 4*u = v
so they are parallel

Answer 8

@perl thank you very much for your explanation :)