Vector help

[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 this(you need an account to see links)

[Ray-Chill]

Thank you all! 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!

[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 @(you need an account to see links) 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
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]

@(you need an account to see links) it's telling me the answer is 1.95578