Question

Determine whether u and v are orthogonal, parallel, or neither. u= (4/3,3/2). v=(-8,-9)

Answer 1

\[u=4/3+j3/2 , v=-8-j9 \]

Answer 2

Now this is a very interesting question:
How to know whether two vectors are orhtogonal (which means perpendicular), parallel, or neither.
remember our formula:\[\overrightarrow{u}*\overrightarrow{v}=|\overrightarrow{u}||\overrightarrow{v}|\cos\theta\]where theta is the angle between them.

Now if the angle between them is theta=0 they point in the same direction, and hence are parallel. That makes the for cos(0)=1, so we get\[\overrightarrow{u}*\overrightarrow{v}=|\overrightarrow{u}||\overrightarrow{v}|\cos\theta=|\overrightarrow{u}||\overrightarrow{v}|\cos(0)=|\overrightarrow{u}||\overrightarrow{v}|\]so when the dot product is equal to the product of the magnitudes of the two vectors they are parallel.

Answer 3

what about perpendicular?
then theta=pi/2
and we get cos(pi/2)=0, hence our formula becomes\[\overrightarrow{u}*\overrightarrow{v}=|\overrightarrow{u}||\overrightarrow{v}|\cos(\frac{\pi}{2})=|\overrightarrow{u}||\overrightarrow{v}|(0)=0\]so if we do the dot product and get zero we find out that the vectors are orthogonal (perpendicular).

Answer 4

If we check both of these facts and neither are true, then they are neither perpendicular nor parallel.

Answer 5

when i did the dot product they were neither the same and did not equal zero.

Answer 6

let me check...

Answer 7

I seem to get neither as well

Answer 8

awesome! thanks so much :)

Answer 9

yw!

Answer 10

wait I may be wrong, I think they are parallel...

Answer 11

yeahh i got that one wrong. lol its okay

Answer 12

Oh, only one chance?
I'll remember to double-check next time :(

Answer 13

its perfectly fine! yeah just once chance

Answer 14

dang sorry,
what I said above is true though, that's how I found out.
Arithmetic error...

Answer 15

its alright! haha still thanks for the help

Answer 16

welcome