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If they all have the same norm.

Q: What circumstances will three vectors be equal in magnitude?

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

Take any three vectors in a plane which, when placed end-to-end form a triangle. The resultant of the three vectors will be zero.

Yes, put the three vectors in a plane, with a separation of 120 degrees between each vector and each of the other vectors.

Yes, if the three vectors are starting from the same point and are directed at 120 degrees between each two vectors.

If both vectors are of the same magnitude, and the resultant is equal to one, then all three are equal. This describes an equilateral triangle.Since the angles of a triangle must sum to 180, the three angles of an equilateral triangle are all 60 degrees.

Related questions

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

Take any three vectors in a plane which, when placed end-to-end form a triangle. The resultant of the three vectors will be zero.

Yes, put the three vectors in a plane, with a separation of 120 degrees between each vector and each of the other vectors.

Yes, if the three vectors are starting from the same point and are directed at 120 degrees between each two vectors.

If both vectors are of the same magnitude, and the resultant is equal to one, then all three are equal. This describes an equilateral triangle.Since the angles of a triangle must sum to 180, the three angles of an equilateral triangle are all 60 degrees.

Yes.

Two vectors: no. Three vectors: yes.

Only if the magnitude of all three vectors equals 0.Suppose three vectors (xi), (xj), (xz) are added. If the above statement is true then adding these three vectors should give a magnitude of x(x2 + x2 + x2)1/2 = xSquaring both sidesx2 + x2 + x2 = x22x2=0The above expression is only solvable for x = 0Hence the answer to the above equation is no, unless both vectors are the zero vector.

Sum of two vectors can only be zero if they are equal in magnitude and opposite in direction. So no two vector of unequal magnitude cannot be added to give null vector. Three vectors of equal magnitude and making an angle 120 degrees with each other gives a zero resultant.

Two vectors, no; three vectors yes.

-- The minimum magnitude that can result from the combination of two vectors is the difference between their magnitudes. If their magnitudes are different, then they can't combine to produce zero. -- But three or more vectors with different magnitudes can combine to produce a zero magnitude.

Magnitude? Yes. Simple answer: think of it as a triangle. Can a triangle have three sides of the same length? Yes. Long answer: there really isn't a long answer. To get the resultant of two vectors, one would add up the components of each vector. While it is impossible to add two vectors of the same magnitude and derive a resultant of the same magnitude AND DIRECTION as one of the vectors, one need only to create a directional difference of exactly 60 degrees between the first two vectors to result in a resultant of like magnitude. Math really is the most perfect language. Vectors are to triangles what optics are to to the study of conics!