Question

let U=<-1,-3> and V=<5,5> . Find -3u+5v

Answer 1

\( -3u+5v=<3,9>+<25,25>=<28,34>\)

Answer 2

you dont add component form like coordinate points?

Answer 3

I'm not certain. One moment.

Answer 4

Well, vector methods are pretty much straight forward.

You multiply a vector by multiplying each of tits elements..

-3u = <-1 * -3, *3 * -3>
5v = well, you get the picture.

And then you just add them element wise.

Answer 5

Limitless is correct.

Answer 6

okay that makes sense!

Answer 7

^Thank you, Vir!

Answer 8

thank you both!

Answer 9

now what about orthagonals?

Answer 10

Gonna need a little more context to know what to do.

Answer 11

okay comming right up

Answer 12

write the vector as a sum of two orthoganal vectors one of which is the vector projection of U onto v, projvU

Answer 13

u=<8,6> v=<2,4>

Answer 14

Okay, orthogonal just means perpendicular. So let's start there. We want to add up two vectors to make that vector we got in the last problem.

Answer 15

so <10,10>

Answer 16

this is a compleatly different problem just to clear that up

Answer 17

Ooh....!

Answer 18

So, we need to find the component of <10,10> in the direction of <8,6>. That's our first priority.

Answer 19

Then we just need to create a perpendicular vector that'll equal us out to <10,10>

Answer 20

okay so the first step is to add the two vectors then?

Answer 21

Yeah,add u and v and we have the sum of the two vectors. We need to write that as two new vectors, which are perpendicular to each other.

Luckily, we have one of our directions already figured out. We just need to find out how long it'll be.

Are you familiar with finding components of vectors?

Answer 22

i should be do you mean like the points that would make up the vector?

Answer 23

I have two vectors, a and b. I want to find the "component"of vector b in the direction of vector a. let's call that vector c.

: