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Pre Cal/Vectors

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Can someone show the steps involved in figuring out this type of problem?

Given the magnitudes of vectors u and v and the angle Ό between them, find the magnitude of the sum u + v to the
nearest tenth and the angle that the sum vector makes with u to the nearest degree.
/u/= 20, /v/= 86, Ό = 90°

The answer is 88.3 and 77deg but I don't know how to get to this. Thanks in advance

  • Pre Cal/Vectors -

    Follow the same method and steps as I showed you in

    http://www.jiskha.com/display.cgi?id=1311551145

    except this one is easier since it forms a right-angled triangle, and your parallogram is a rectangle.

    If the resultant is R, then
    R^2 = 20^2 + 86^2
    = 7796
    R = √7796 = 88.29

    Now use the Sine Law again to get the angle between vectors

  • Pre Cal/Vectors -

    X = 20.
    Y = 86.

    tanA = Y/X = 86/20 = 4.3,
    A = 76.9 deg.

    R = X / cosA = 20 / cos76.9 = 88.24

    OR
    R = Y / sinA = 86 / sin76.9 = 88.3
    .

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