Question

Find the unit vector having the same direction as v.
v = -5i + 12j

Answer 1

so far I have:

Answer 2

\[v = -5i+12j\]\[||v|| = \sqrt{(-5)^2 + 12^2}\]\[||v|| = \sqrt{25 + 144}\]\[||v|| = \sqrt{169}\]\[||v|| = 13\] So: \[u = \frac{ -5i+12j }{ 13 }\]\[u = \frac{ -5 }{ 13 }+\frac{ 12 }{ 13}\] Therefore: \[||u|| = \sqrt{(\frac{ -5 }{ 13})^2+(\frac{ 12}{ 13})^2}\]\[||u|| = \sqrt{\frac{ 25 }{ 169 }+\frac{ 144 }{ 169 }}\]\[||u|| = \sqrt{\frac{ 169 }{ 169}}\]\[||u|| = 1\]

Answer 3

we want to scale it by some number: k, such that

(5k)^2 + (12k)^2 = 1

Answer 4

you did fine

Answer 5

I know the answer is not, \[||u|| = 1\] is it \[u = \frac{ -5 }{ 13 }i+\frac{ 12 }{ 13 }j\]?

Answer 6

i can do the math, but I am not 100% of which answer it wants

Answer 7

its the scaled version of u, the divide by 13 stuff

Answer 8

so, finding the magnitude of u is just extra?

Answer 9

its not asking for the length of the unit vector

its asking for the vector itself, that has a length of 1 and is in the same direction as u

well, any positive scalar of u is in the same directions as u

Answer 10

no, u is 13 units long ... we want it 1 unit long

13/13 = 1

Answer 11

awesome, once again thank you! I doubt myself a lot.

Answer 12

consider a triangle

Answer 13

similar triangles

1:13 a:5 b:12

what are a and b?

Answer 14

they should be a ratio of the sides they parallel, no?

Answer 15

oh

no

Answer 16

1

Answer 17

1=a^2 + b^2

Answer 18

we scaled 13 down to 1 ... how? divide by 13

a = 5/13 b = 12/13 since 1=13/13

Answer 19

ignore what i said just now. i had a stroke, not a stroke of genius xD

Answer 20

a:b:c

5:12:13 c = 1 tho, divide by 13 to scale the ratio

5/13 : 12/13: 13/13

Answer 21

lol

Answer 22

Thank you for your over the top help!

Answer 23

yep in short, a unit vector is just the vector scaled so its length is 1

Answer 24

yay for learning!