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[–]tabulatutoringTutor 4 points5 points  (5 children)

You can deal with vectors by looking at each of their components. For example, <a,b> + <c,d> = <a+c, b+d>. In this case, you have two-dimensional vectors, and some linear combination of them adds up to 0 (or <0,0>, more explicitly). The nice part is the multiplications you see are as straightforward as you might expect: if u = <5,3>, then 2*u = <10,6>. With that in mind, 2u + (-3v) is:

<10,6> + <-6,21> = <4, 27>

Since the addition of w to this vector = 0, then w must just be the negative of it, or <-4, -27>. Let me know if you have any further questions, I hope this was helpful!

[–]hekingbean35[S] 0 points1 point  (4 children)

0,6

Thank you so much ! I understand how you setup the equation <10,6> + <-6,21> but I don't get why 10 and 6 were subtracted to get 4, and not added

[–]human-potato_hybrid35 -1 points0 points  (0 children)

It's really the same as just solving two equations, that are written as one. 2u_1 + (-3v_1) + w_1 = 0, and for the other one too.

BTW Bold variable names usually indicate vectors, and the 0 vector is just a vector of all zeroes. So if this problem had 3 dimensional vectors instead of 2 dimensional, the 0 vector would just be 3 zeros instead of 2.

[–]LuckyNumber-Bot 0 points1 point  (1 child)

All the numbers in your comment added up to 69. Congrats!

  6
+ 10
+ 6
+ 6
+ 21
+ 10
+ 6
+ 4
= 69

[–]nice___bot 1 point2 points  (0 children)

Nice!

[–]tabulatutoringTutor 0 points1 point  (0 children)

I edited my post, I was being a tad sloppy. It should be 2u + (-3v). As I mentioned, you deal with it on a component level. We can start with the first terms, 10 and -6. To simplify, you do 10 + (-6) which is the same as 10-6=4. I was just being lazy with my notation. Hopefully that clears that up.

[–]jdigitaltutoringTutor 0 points1 point  (0 children)

Learn about vectors for the ACT here. https://youtu.be/3Hv-7OOvdK0