Question

Let u = <-4, -3>. Find the unit vector in the direction of u, and write your answer in component form.

Can someone help please!

Answer 1

unit vec = vec divided by its magnitude
1. find its magnitude
2. divide each component by that number to give you a unit vector

Answer 2

@electrokid would the magnitude be 1?

Answer 3

no
sqrt(ax^2+ay^2)

Answer 4

Here's a blank xy axis

Answer 5

ax= -4, ay= -3

Answer 6

now add on the vector <-4, -3>

Answer 7

so you basically have this triangle



and you want to solve for x

Answer 8

@jim_thompson5910 so would you put it over 7?
-4/7,-3/7?

Answer 9

no you don't add 4 and 3 to get 7

Answer 10

so x is not 7

Answer 11

you solve for x using the pythagorean theorem

Answer 12

a^2 + b^2 = c^2

3^2 + 4^2 = x^2

...
...

x = ??

Answer 13

@jim_thompson5910 over 25!

Answer 14

closer, but no

Answer 15

x is not 25 but it is....

Answer 16

what is x?

Answer 17

@jim_thompson5910 if its x^2 then wouldnt it be 625?

Answer 18

x^2 = 25

so

x = 5

Answer 19

so we can say

Answer 20

and the magnitude of the vector is 5 units

Answer 21

@jim_thompson5910 ohhh, I had it wrong :\ its a 3,4,5 triangle

Answer 22

so the unit vector in component form is

\[\Large -\frac{4}{5}i - \frac{3}{5}j\]

Answer 23

@jim_thompson5910 thank you!!!

Answer 24

yw