Two force vectors,
F1 = (-3.0 N) x-hat + (-2.5 N) y-hat
and
F2 = (-6.0 N) x-hat + (3.5 N) y-hat
are applied to a particle. What third force F3 would make the net force on the particle zero?

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Are you familiar with the bra -ket vector notation
F1 = = < -3 , -2.5>
?

Nope. :0

ok, it is just that, the x and y components

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