Question

Determine whether u and v are orthogonal, parallel, or neither: u=(1,7), v=(-42,3)

Answer 1

do you know their dot product?

Answer 2

i think that their dot product is -63

Answer 3

so it's not orthagonal...

Answer 4

the dot product is not -63

Answer 5

oh yea

Answer 6

dot product = 1*(-42)+7*3 = -21

Answer 7

but because the dot product isn't 0, the two vectors are not orthogonal (they don't form a 90 degree angle)

Answer 8

oh, sorry i accidentally typed the wrong number... but its still not orthogonal

Answer 9

yes in both cases they're not orthogonal

Answer 10

but how do i know if it is parallel or not?

Answer 11

parallel vectors are two vectors u = (a,b) and v = (c,d)

such that v = k*u = k(a,b) for some scalar k

Answer 12

So if you can show that (c,d) = (ka,kb), then the two vectors are parallel

Answer 13

what is k?

Answer 14

k is any scalar number

Answer 15

so in this case

(-42,3) = (k*1, k*7)

can you find a single value of k that works here?

Answer 16

dot product = uvcosA
A is the angle b/w u and v
if orthogonal, A=90
so dot product(DP) = 0 since cos90 = 0
if they are parallel, A=0
DP = uv, since cos0 = 1
and else they are neither orthogonal nor parallel

Answer 17

i don't think so

Answer 18

so because there are no solutions to (-42,3) = (k*1, k*7), the two vectors are NOT parallel

Answer 19

Ok, I think I get how you found that!

Answer 20

that's great

Answer 21

ok heres the deal with this problem, I will tell you exactly how to do this! Ok so in parallel the answer is either 1 or -1 if its orthogonal the answer is 0 and neither would be Anything that isnt 1,-1, or 0.


To do this problem

V*W
-------
IIVII*IIUII



Lets first find v*u


1*(-42)+7*3 = -21

now lets find magnitude v * magnitude u

to find magnitude V we just take that square root of the numbers in v so.....
sqr((-42)^2+(3)^2
=42.10

now lets find the magnitude of W

sqr((1)^2+(7)^2
=7.07


plug this into our original equation

Answer 22

sorry that is

V*U
-------
IIVII*IIUII

Answer 23

V*U
-------
IIVII*IIUII

-21
------
(42.10)(7.07

=-0.07

so its neither!

Answer 24

@violin37 why wats the problem...???

Answer 25

don't worry about it, i got my answer

Answer 26

ohk...

Answer 27

Please use my way as it is much easier to understand!