Question

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

u = <10, 6>, v = <9, 5>

Answer 1

Orthogonal

Parallel

Neither

Answer 2

@TuringTest

Answer 3

the dot product determines the relative orientation of two vectors\[\vec u\cdot\vec v=\|\vec u\|\|\vec v\|\cos\theta_{uv}\]

Answer 4

theta is the angle between u and v.
when two vectors are parallel, the angle between them is zero, and the formula reduces to\[\vec u\cdot\vec v=\|\vec u\|\|\vec v\|\]so if the dot product of two vectors is euqla to the product of their magnitudes, they are parallel

Answer 5

equal*

Answer 6

similarly, if they are orthogonal the angle between them is pi/2, the cosine of which is zero, so the formula reduces to\[\vec u\cdot\vec v=0\]hence if the dot product between them is zero then they are orthogonal

Answer 7

if neither of the above is true then they are neither parallel nor orthogonal

Answer 8

so in this case?

Answer 9

what do you get when you do the dot product?

Answer 10

how do i do that? im not well at math?

Answer 11

@TuringTest

Answer 12

me thinks you have been skipping lessons...\[\vec u=\langle a_1,b_1\rangle\]\[\vec v=\langle a_2,b_2\rangle\]\[\vec u\cdot\vec v=a_1a_2+b_1b_2\]

Answer 13

take the dot product - if its zero, then they are orthogonal
if not, see if one is a multiple of the other - if so they are parallel
if not, neither

Answer 14

yes, that is a faster way to check that they are parallel, goo point @gregohb

Answer 15

good*

Answer 16

but how do i take the dot product??

Answer 17

read 4 posts up, I wrote the formula

Answer 18

multiply each respective component and add the results