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

Question

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

anonymous · Answer

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

amistre64 · Answer

what is the length of the given vector?

amistre64 · Answer

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

anonymous · Answer

that's all that's given :\

anonymous · Answer

12? lol

amistre64 · Answer

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

amistre64 · Answer

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

amistre64 · Answer

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?

anonymous · Answer

I did that and got sqrt 79, yes?

amistre64 · Answer

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

amistre64 · Answer

18+10=28 .. not 29 :)

anonymous · Answer

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

amistre64 · Answer

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)

amistre64 · Answer

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

anonymous · Answer

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!!