Vector help

[Ray-Chill]

So we learned vectors in class and i'm still so confused.

Can anyone explain how to do a few problems, and maybe what these are about. I will +rep for helpers!


New::
An airplane needs to head due north, but there is a wind blowing from the southwest at 40 km/hr. The plane flies at an airspeed of 800 km/hr,

To end up due north, the pilot will need to fly the plane ______ degrees west of north

----------------------------------------

As part of video game, the point (2,1) is rotated counterclockwise about the origin through an angle of 35 degrees.

Find the new coordinates of this point

[Ana]

Rayray, I'd help, but I can't read the instructions xD

[lucygoose]

That's a very small image. Could you type out the instructions please? :3

[Ray-Chill]

Yes. :P
Sorry about that.

"Write the vector shown below as a combination of vectors u→ and v→ shown above"

[Aeires]

okay so the key to vectors is the size and the direction that the line is going, if the vector you are asked to describe goes in the opposite direction of one of the given vectors than it is the negative vector. That's the basics of vectors i can find some online examples for you if you want?

[Ray-Chill]

Yes please. I'm just confused about how to add them up and junk.. I don't understand how two of them add up to the other one.

[lucygoose]

I am completely stumped, sorry I can't help :(

[Ray-Chill]

Lol It's alright. Thank you for trying!
:)

I'll be posting more soon, if I can't figure them out.

[bamag]

Break down v to x and y components. v = {-1, 2}
do same for u: {1, 1}
The resulting vector components are {2, -7}
Then you find scalars that make the components add up
m{-1,2}+n{1,1}={2,-7}
-m+n=2
-2m+2n=4
2m+n=-7
3n=-3
n=-1
m=-3
So the two numbers you would put in would be -3, and -1

[Ray-Chill]

Break down v to x and y components. v = {-1, 2}
do same for u: {1, 1}
The resulting vector components are {2, -7}
Then you find scalars that make the components add up

What do you mean by making them add up?

[Aeires]

Adding vectors is just adding lines head (arrow head) to tail of the vector being added. So in you're example vector u+v would be the line that connects the two vectors to make it a triangle. so with that said i think the answer to the example is u+3v. How i got there was putting three v vectors from the arrow head down along the line which puts you exactly one unit away from the end of the arrow which is the same size as the u vector given in the first part

[bamag]

Vector v goes up 2 and to the left 1 so the xy components are <-1,2>
other vector goes up 1 and right 1 so <1,1>
the resulting vector goes down 7 and right 2 so <2, -7>
Let m and n be two real numbers
m*<-1,2>+n*{1,1>=<2,-7>
You turn this into the equations:
-m+n=2 (from the x components}
and
2m+n=-7 (from y)
Then you solve the system of equations to get answer.
m=-3 n=-1
-u + -3v = the vector

[Aeires]

is you want to do it graphically just draw the vectors onto the graph like this3540

[Ray-Chill]

Thank you all! :P I figured that part out! xD only took me forever..

Thank you!

I might be posting some more.
but let me know if I missed the +rep! :P

[Ray-Chill]

New problem:

ahh..


An airplane needs to head due north, but there is a wind blowing from the southwest at 40 km/hr. The plane flies at an airspeed of 800 km/hr,

To end up due north, the pilot will need to fly the plane _____ degrees west of north

-----------------------------------------

As part of video game, the point (2,1) is rotated counterclockwise about the origin through an angle of 35 degrees.

Find the new coordinates of this point

[Aeires]

I think the answer to the first one is 89.7 degrees. I think you use the dot product to find the angle and this equation a.b = |a| |b| tan A where a = the 40km wind, b is 800km of the plane and A is the angle between the 2 vectors.

[Ray-Chill]

Thank you Aeires but it's saying that's wrong.

[Aeires]

hummmm let me try again it's been a few years since i have done 2 space vectors

---------- Post added at 02:40 AM ---------- Previous post was at 02:19 AM ----------

2.87 degrees is that right ? i was using the wrong formula it's sin-1(wind speed/travel speed) i think

[bamag]

An airplane needs to head due north, but there is a wind blowing from the southwest at 40 km/hr. The plane flies at an airspeed of 800 km/hr,
To end up due north, the pilot will need to fly the plane _____ degrees west of north
Flying north means x component = 0
x component of wind is sin45 * 40km = 28.28km
x component of plane is sintheta * 800km
0 = 28.2 + sintheta *800
sin theta = -28.28/800
arcsin -28.28/800 = -2.02 degrees
So answer is 2.02 degrees
I think im wrong :D
nvm I think I'm right :p

As part of video game, the point (2,1) is rotated counterclockwise about the origin through an angle of 35 degrees.
Find the new coordinates of this point
Formula is (x',y')=(xcostheta-ysintheta, xsintheta+ycostheta)
(2cos35-sin35, 2sin35+cos35)= (1.065, 1.966)

[Ray-Chill]

bamag it's telling me the answer is 1.95578

[bamag]

for 1st problem?