×

# Vectors approximate sum

1.  Junior Member
Join Date
May 2016
Posts
7
Reputation ## Vectors approximate sum

What is the approximate sum of the following two vectors? Magnitude 20 at 30° and magnitude 10 at 60°.  Reply With Quote

2. Originally Posted by rasilva What is the approximate sum of the following two vectors? Magnitude 20 at 30° and magnitude 10 at 60°.

First you have to convert to rectangular (Cartesian)

x=r*cosθ and y=r*sinθ

x1=20 cos(30) = 17.32
y1= 20 sin(30) = 10
x2=10 cos(60) = 5
y2= 10 sin(60) = 8.66

x3= x1+x2 = 22.32
y3= y1+y2= 18.66

Now convert back to polar:

r=sqrt((x^2)+(y^2)) tanθ=(y/x)

r=sqrt((22.32)^2+(18.66)^2) = 29.09

θ=tan^(-1) (18.66/22.32) = 39.9

Thus we end up with an answer of:
29.09<39.9o

So, in general, you can add/subtract rectangular forms.
You can also multiply/divide polar magnitudes(angles are added when multiplying and subtracted when dividing).

Great references for this math below:

https://www.mathsisfun.com/polar-car...ordinates.html  Reply With Quote

electrical calculations, neta exam questions, neta level 3 Related Content 