## nthenic_oftime one year ago please help.. idk how to even figure this out so steps would be nice too. Find the specified vector or scalar. u = -4i + 1j and v = 4i + 1j; Find . ||u+v|| A. Sqrt34 B. 8 C. 5 D. 2

1. phi

first add the "corresponding" terms then find the length of the resulting vector (length is sqrt(sum of square of each term))

2. phi

for example the length of 3i+4j is $\sqrt{3^2+4^2} = \sqrt{9+16}= \sqrt{25} = 5$

3. nthenic_oftime

hey thank you for that a answer can you show me how you got got the length of the vector

4. phi

what did you get for u+v?

5. nthenic_oftime

wait i misunderstood i thought that was the same thing. im so confused

6. nthenic_oftime

first add corresponding terms gives us... i+2j ?

7. nthenic_oftime

idk how to find the length of a vector

8. phi

-4i + 1j 4i + 1j

9. phi

-4i + 4i is not i

10. nthenic_oftime

its 0?

11. nthenic_oftime

i dont understand the whole vector and scalar thing

12. phi

yes, the i's "go away" you are left with 2j

13. nthenic_oftime

which is positive points?

14. phi

in 2-dimensions, you can think of the vector as <x,y> pair of numbers for example, u= -4i + 1j (which can also be written <-4,1> in a graph, it looks like this: |dw:1443634973472:dw|

15. phi

and the length of the vector is the length of the line from (0,0) (the origin) to the point (-4,1) we use pythagoras to find its length

16. nthenic_oftime

okay so U is a vector and length would be to the point.

17. nthenic_oftime

oh okay i didnt see your message

18. phi

u+v = 2j (or 0i+2j, or (0,2) ) in a graph it looks like this |dw:1443635111360:dw|

19. nthenic_oftime

|dw:1443635167339:dw|

20. phi

we could use pythagoras $\sqrt{0^2+2^2}= \sqrt{0+4}= \sqrt{4}= 2$ but we can see the length is just 2

21. nthenic_oftime

oh cool good so our drawings of vthis match okay so 0^2 because we have no i left and 2^2 becayse 2j

22. nthenic_oftime

i understand thank you so much... can i ask what do i and j standfor why not use x and y? i got behind and i am trying to catch up on things as its obvious i am missing a gfew things in my knowledge

23. phi

The interesting thing is this same idea works for 3-D or even higher dimensions (though visualizing a vector with more than 3 components is beyond me)

24. phi

I'm not sure why people use i,j,k but it does not matter the idea is they are different "dimensions" for example, sideways and up/down. The other way people write vectors is as a "tuple" such as (1,2) or <1,2> where it is understood each number is the distance along each dimension

25. nthenic_oftime

okay so vectors would be written as plot points or coordinates just signified as different dimensions thanks for the help on the problem and that little info there it caught me up a lil bit. medal and fan for you :)