Understanding Resultant: When is a Resultant Zero in First Quadrant Vectors?

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In summary, the conversation discusses the possibility of a resultant vector being zero when three vectors are positioned in the first quadrant of an x-y coordinate system. It is determined that as long as the vectors originate from the same point, their sum cannot be zero. However, it is noted that sometimes vectors may be inaccurately represented in a quadrant system, resulting in a misleading zero sum.
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dg_5021
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When is a resultant zero? When three vectors are on the first quadrant of an x-y coordinate system does that resultant be zero?
 
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Think about what you are asking. If you add three positive numbers is it possible for their sum to be zero? :-)
 
  • #3
As long as you three vectors all start witht heir tails in the origin, then their sum cannot be zero. BUT sometimes teachers are sloppy in their representations of vectors: It is possible to draw three vectos in the first quadrant ofa x-y graph such that their sum is zero (they would form a closed triangle with all arrows pointing either clockwise or ccw); but this would be due to a misrepresentation of vectors in a quadrant system.
 

1. What is a resultant in first quadrant vectors?

A resultant is the sum of two or more vectors in the first quadrant, which represents the overall effect or direction of the combined vectors.

2. How is a resultant calculated in first quadrant vectors?

To calculate a resultant in first quadrant vectors, you can use the Pythagorean theorem or the parallelogram method. The Pythagorean theorem involves finding the square root of the sum of the squares of the horizontal and vertical components of the vectors. The parallelogram method involves drawing the vectors as sides of a parallelogram and finding the diagonal, which represents the resultant.

3. When is a resultant zero in first quadrant vectors?

A resultant is zero in first quadrant vectors when the vectors cancel each other out, meaning their magnitudes and directions are equal and opposite.

4. Can a resultant be negative in first quadrant vectors?

No, a resultant cannot be negative in first quadrant vectors. Since the first quadrant only includes positive values, the resultant will always be positive or zero.

5. What is the significance of a zero resultant in first quadrant vectors?

A zero resultant in first quadrant vectors indicates that the combined vectors have no overall effect or direction. This could mean that the vectors are balanced or that they cancel each other out.

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