###### Asked in Math and ArithmeticPhysicsAlgebra

Math and Arithmetic

Physics

Algebra

# Is it is possible to add three vectors of equal magnitude and get zero?

## Answer

###### Wiki User

###### June 12, 2015 6:14PM

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

###### Asked in Math and Arithmetic, Physics, Algebra

### Can three vectors of equal magnitudes be added to give a vector of same magnitude and how?

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 = x
Squaring both sides
x2 + x2 + x2 = x2
2x2=0
The above expression is only solvable for x = 0
Hence the answer to the above equation is no, unless both
vectors are the zero vector.

###### Asked in Science, Math and Arithmetic, Physics

### Can the resultant of two vectors of the same magnitude be equal to the magnitude of either of the vectors?

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!

###### Asked in Math and Arithmetic, Physics, Algebra

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

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>.

###### Asked in Physics

### Under what conditions the sum of three vectors will be zero?

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.

###### Asked in Math and Arithmetic, Physics, Algebra

### Can three vectors not in one plane give zero resultant?

No. For three vectors they must all lie in the same plane.
Consider 2 vectors first. For them to resolve to zero, they must be
in opposite direction and equal magnitude. So they will lie along
the same line.
For 3 vectors: take two of them. Any two vectors will lie in the
same plane, and their resultant vector will also lie in that plane.
Find the resultant of the first two vectors, and the third vector
must be along the same line (equal magnitude, opposite direction),
in order to result to zero.
Since the third vector is along the same line as the resultant
vector of the first two, then it must be in the same plane as the
resultant of the first two. Therefore it lies in the same plane as
the first two.