Question

How do I Find a unit vector in the direction of w=(-4,6)

Answer 1

Do you want the magnitude and direction?

Answer 2

Magnitude =\[\sqrt{y^2+x^2}\]

Answer 3

direction

Answer 4

to make you vector into a unit vector you divide it by the magnitude
the direction will not change

Answer 5

The angle would be between180 and 90 degrees (not sure what quadrant that is)

Answer 6

your*

Answer 7

so tan(4/6) equals direction, but I am not sure if tan is positive or negative in that quadrant.

Answer 8

"How do I Find a unit vector in the direction of w=(-4,6)"
doesn't ask for an angle, it just asks for the unit vector that points in the same direction, so just divide your original vector by the formula snipa gave you

Answer 9

Well, a vector, by definition, has both magnitude AND direction.

Answer 10

and it would be arctan(-2/3) for direction if you did want to know it

Answer 11

Yeah, @TuringTest is right. It is arctan to find the angle. Sry

Answer 12

yes I agree, so you don't need to specify the angle unless they ask for it

Answer 13

no apologies necessary :)
the point is that the unit vector is the original vector divided by the magnitude.
Do you understand that @parksbap ?

Answer 14

and tan(x) is positive in the first and second quadrants (between 0 and 180 degrees)

Answer 15

yes and no

Answer 16

a little confusing but im catching it

Answer 17

The direction would be 146.3 degrees. I think

Answer 18

do you know how to find the magnitude of this vector?

Answer 19

no

Answer 20

Loook at my first formula

Answer 21

@Snipa420 please try not to just shoot out numerical answers; that's not the goal of this site.

Answer 22

i agree, i need to be shown how to do this for a test

Answer 23

but yes, @Snipa420 has given the correct formula for the magnitude

Answer 24

ok first formula get it!

Answer 25

@TuringTest She needs to see how to find the direction as well, I think. Is that right, @parksbap

Answer 26

so you should be able to take that, plus what I told you, and get the answer
first: what is the magnitude?

Answer 27

yes so i did the magnitude, i got \[\sqrt{52}\]

Answer 28

so since there is only a decimal i need to break that down

Answer 29

Yup

Answer 30

so from that i have 4\[\sqrt{13}\]

Answer 31

\[\sqrt{52}=\sqrt{4\times13}=2\sqrt{13}\]

Answer 32

It would be\[\sqrt{4}*\sqrt{13}\]

Answer 33

ok

Answer 34

ok, so now you just divide the vector you have by that, and that is your unit vector
we can discuss the direction in radians or degrees again after that if you want...

Answer 35

well the answer is -2/\[\sqrt{13} \] and 3/\[\sqrt{13}\]

Answer 36

right
and if you still need direction that's given by\[\tan^{-1}(\frac yx)\]
since the unit vector points in the same direction as the original, you can use the original x and y in the formula

Answer 37

@TuringTest , arctan(y/x) does not give you the real direction. It gives you a number that you must interpret further.

Answer 38

how so??

Answer 39

Just take arctan(y/x). YOu get around 33 degrees.

Answer 40

You must then observe that because the point is in the 2nd quadrant(-4, 6), that 33 degrees is not the right answer

Answer 41

\[\tan\theta=\frac yx\implies\theta=\tan^{-1}(\frac yx)\]ah yeah you're right about the whole adding \(\pi n\) thing, must have slipped my mind
my mistake

Answer 42

No, you dont add Pi/n either.

Answer 43

you add pi...

Answer 44

How I got to my answer is I saw that it was in the second quadrant, and thus did 180 degrees - arctan(y/x), and got THE RIGHT ANSWER.

Answer 45

Again, no you do not. If you add Pi, you will get an angle in the third quadrant.

Answer 46

The angle we are looking for is in the second quadrant.

Answer 47

I get -33 deg on my calc, so addin 180 puts me in QII

Answer 48

Oh ok. YOu are right.

Answer 49

\[\tan^{-1}(-2/3)\approx-33.69\]teamwork!

Answer 50

I just took arctan(y/x), like you previously said, and then did 180-that answer.

Answer 51

So we got the Same answer!!! Nice. My bad for doubting your maths skillz

Answer 52

so yeah, just add pi
why? because tan never changes when you add \(\pi n\) if n is an integer

Answer 53

it's all good, my math skills may exist, but my fatigue always could use a second set of eyes
thanks Snipa

Answer 54

you are right, you are right...

Answer 55

Yeah no problem. Later