Question

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

u = <7, 2>, v = <21, 6>

Answer 1

@bibby @cwrw238

Answer 2

do you know how to compute the dot product?

Answer 3

yeah, it should be 159

Answer 4

ok, so what does that tell you?

Answer 5

I have no clue

Answer 6

it tells you they are not perpendicular, because if two vectors are perpendicular the dot product between them is zero. so that rules out one possibility.

Answer 7

two vectors are parallel if one is a scalar multiple of the other (because multiplying a vector by a scalar just makes it longer, it doesn't change it's direction)
is one of these vectors a scalar multiple of the other?

Answer 8

what's a scalar multiple?

Answer 9

multiplied by a non-vector number
i.e. say we have a vector <1,2>
then the vector <4, 8> is parallel to <1,2> because it is a scalar multiple of it by a factor of 4

Answer 10

kinda like a ratio?

Answer 11

yeah, that is one way to say it
if each component from each of the vectors have the same ratio, the vectors are scalar multiples of each other

Answer 12

okay, so it is by a factor of 3

Answer 13

4/1=4
8/2=4
hence the two vectors in my example are parallel because one is 4 times the length of the other, in the same direction

Answer 14

correct

Answer 15

so they're parallel?