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A vector has both magnitude and direction. The magnitude is always positive, by convention, but this is not cast in stone. So you can have in your case a positive magnitude with a direction 257.31 degrees, which is the same as a positive magnitude 77.31 degrees in quadrant III, but the first way is more conventional. One could also say a negative magnitude at 77.31 degrees, in which case the negative sign implies a 180 degree reversal.

So there are many choices, and you seem to have a good handle on this.

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Q: Can a vector resultant have a negative direction I have a statics problem and the answer is 77.31 deg in the III quad Negative or Positive Or is the answer 257.31 deg from the horizonal?
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