Best Answer

Yes.

Two vectors that have equal magnitude and point in opposite directions have a sum of zero. (Like <1,0> and <-1,0>, one pointing in the positive x direction and one in negative x direction.

The same idea applies with three vectors. For example, <1,0,0>, <-1,1,0> and <0,-1,0> have a sum of <0,0,0>.

Q: Can the sum of two or three vectors ever be zero?

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If three vectors form a triangle , their vector sum is zero.

Three vectors are coplanar if they sum to zero. V1 + V2 + V3 = o means the three vectors are coplanar.

The orientation of the three vectors that sum to zero must be coplanar, contained in the same common plane, including being contained in a common line in a plane.

With three vectors spaced 120 degrees apart and with identical magnitudes the vector sum will be 0.

Yes. Vectors contain both magnitude and direction. Graphically three vectors of equal magnitude added together with a zero sum would be an equilateral triangle.

Related questions

If three vectors form a triangle , their vector sum is zero.

Vectors that sum to zero are coplanar and coplanar vectors sum to zero.

Three vectors are coplanar if they sum to zero. V1 + V2 + V3 = o means the three vectors are coplanar.

The orientation of the three vectors that sum to zero must be coplanar, contained in the same common plane, including being contained in a common line in a plane.

With three vectors spaced 120 degrees apart and with identical magnitudes the vector sum will be 0.

Three vectors sum to zero under the condition that they are coplanar (lie in a common plane) and form a triangle. If the vectors are not coplanar, they will not sum to zero. Another way of looking at it is that the sum is zero if any vector is exactly equal in magnitude and opposite in direction to the vector sum (so-called resultant) of the remaining two.

Yes. Vectors contain both magnitude and direction. Graphically three vectors of equal magnitude added together with a zero sum would be an equilateral triangle.

No, they cannot sum to zero.

Two is the minimum number of vectors that will sum to zero.

The result is a zero vector. If the sum of the vectors forms a closed figure, the vectors sum to zero.

When the angle between two vectors is zero ... i.e. the vectors are parallel ... their sum is a vector in thesame direction, and with magnitude equal to the sum of the magnitudes of the two original vectors.

No. The largest possible resultant magnitude is the sum of the individual magnitudes.The smallest possible resultant magnitude is the difference of the individual magnitudes.