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Vectors approximate sum

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    Vectors approximate sum

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

    Please explain

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

    Please explain
    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

    Now add them together:

    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
    https://www.allaboutcircuits.com/tex...er-arithmetic/

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