Question

Find the specified vector or scalar.

u = -4i + 1j and v = 4i + 1j; Find ‖u+v‖.

Answer 1

A. √34
B. 8
C. 2
D. 5

Answer 2

Well do we know how to do the u+v part or should we go over that part, too?

Answer 3

go over it ..i dont know how to.

Answer 4

Alright. So you can see the vectors have an i part and a j part. When we add or subtract vectors, we combine the i parts and the j parts. So combining the i parts, we are doing
-4i + 4i and for the j we have
1j + 1j.
So this is just combining like terms to leave us with simply 2j.
That make sense?

Answer 5

yes makes sense.

Answer 6

Alright, cool. Now the || || part means magnitude. It essentially just wants the length of the vector. Now we find the length the same way we would find the hypotenuse of a triangle or the distance between two points, with pythagorwan theorem/distance formula. If we recall, this is:
\[c = \sqrt{a ^{2}+b ^{2}} \] Except this time we have i and j instead. Doesn't matter, process is the same. So now we do this:
\[||u+v|| = \sqrt{(0)^{2}+(2)^{2}}\] I leave the i and the j out because we are only conncerned about the numbers. So if we do that calculation, what do we get?

Answer 7

you get \[\sqrt{4}\] ??

Answer 8

Yep, which reduces to 2. So your magnitude is just 2. Which makes sense. Before we took the magnitude, we just had 2j. Well, all that means is we go 0 units right and 2 units up



which this naturally has a length(magnitude) of 2 :3

Answer 9

okay .. than anything else.

Answer 10

No, that's all that was needed. We added u and v to get 2j, then did distance formula to see that our magnitude was just 2.

Answer 11

okay thought so makes sense(:

Answer 12

Okay, cool ^_^