## KatClaire 2 years ago Find a unit vector in the same direction as u= [3,0,-7,-4,2] (column)

1. KatClaire

$\left(\begin{matrix}3 \\ 0\\-7\\-4\\2\end{matrix}\right)$

2. amistre64

what is the length of the given vector?

3. amistre64

suppose you have a vector that is 12 feet in length, how do you find out its "unit" length?

4. KatClaire

that's all that's given :\

5. KatClaire

12? lol

6. amistre64

yeah, and to find the length of a vector, you square the parts, add em up, and sqrt it all ....

7. amistre64

$vector:<a,b,c,d,...,k>$$distance=\sqrt{a^2+b^2+c^2+d^2+...+k^2}$

8. amistre64

parts: square 3: 9 0: 0 7:49 4:16 2: 4 --- sum: 78 ; so length must be sqrt(78) or did i do something wrong?

9. KatClaire

I did that and got sqrt 79, yes?

10. amistre64

vector = sqrt(78) units to find a vector of 1 unit, we divide both sides by sqrt(78) vector/ sqrt(78) = sqrt(78)/sqrt(78) units vector/ sqrt(78) = 1 unit therefore, a unit vector is created by dividing the components of the vector by its length

11. amistre64

18+10=28 .. not 29 :)

12. bmelyk

sorry my computer like died so I'm on my friends lol so it's 6/sqrt78 @amistre64 then you times that into each unit thingy

13. amistre64

each component then gets divided by the vectors length to obtain components of the unit vector. 3/sqrt(78) 0/sqrt(78) - 7/sqrt(78) - 4/sqrt(78) 2/sqrt(78)

14. amistre64

another way to notate it is just to scale the original vector by 1/length $\frac{1}{\sqrt{78}}[3,0,-7,-4,2]$

15. KatClaire

oh okay my problem was accepting the fact that my calculator wouldn't put my answers in fractions so I thought I must be wrong hahaha. Thanks!!