Question

If u=1 and v=5, and the vectors make the angles of 130 and 180 degrees with the x-axis respectively, find the component form of the sum of u and v.

Answer 1

First find the x,y components for vectors u and v, then you can just add the vectors together by adding their respective components

to go from polar to coordinate:
x = r*cos(theta)
y= r*sin(theta)

where r is the magnitude of each vector, 1 and 5 respectively

Answer 2

use de moivre's theorem

Answer 3

de moivre's theorem should do the trick

Answer 4

u=1+j0, v=5+j0

Answer 5

how does de'Moivres theorem apply to adding vectors

Answer 6

\[like this z=x+jy =r(\cos(\theta)+jsin(\theta))\]

Answer 7

\[u=1+j0 = r=\sqrt{1^2+0^2}= 1\]

Answer 8

\[\theta=130 \]

Answer 9

\[\theta=\tan^{-1} (y/x) = \tan^{-1} (0/1)+\pi\]

Answer 10

r<0 = 1<180

Answer 11

\[v= 5+j0 = r=\sqrt{25}=5\]

Answer 12

\[\theta= 180\]

Answer 13

yo ?

Answer 14

\[u=1(\cos(130)+jsin(130)) =-0.643+j0.77\]

Answer 15

\[v=5(\cos(180)+jsin(180))= -5+0=-5\]

Answer 16

u+v =-5.643+j0.77

Answer 17

are u sure the angles are for u and v respectively ?

Answer 18

ok
basically same thing as converting the coordinates

x = r*cos(theta)
y= r*sin(theta)

u = <cos(130), sin(130)>
v = <-5, 0>

u+v = <-5+cos(130), sin(130)> = -5.63i +0.77j

Answer 19

is i not the same as j ?

Answer 20

u=1<130, v=5<180 in polar form

Answer 21

i is x-part, j is the y-part, when talking about rectangular coordinates