physic

Three forces act on an object with
F1 = (6.03i + 11.17j) N
and
F2 = (2.19i − 13.53j) N.
If the net force on the object is zero, what is the unknown force,
F3?
(Express your answer in vector form.)
F3 =
N

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  1. Let's take F3 as (xi + yj)N

    The sum along each component of all three force vectors is zero, so:

    (6.03 + 2.19 + x)i = (0)i
    => 8.22 + x = 0
    => x = -8.22

    (11.17 - 13.53 + y)j = (0)j
    => -2.36 + y = 0
    => y = 2.36

    So, F3 is given by (-8.22i + 2.36)N

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  2. F1 + F2 = (6.03i+11.17j)+(2.19i-13.53j) = (8.22i - 2.36j.

    F3 = -(F1+F2) = -(8.22i-2.36j) = -8.22i + 2.36j.

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