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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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    29 @ 40 degrees

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