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.
In order for two vectors to add up to zero:-- their directions must be exactly opposite-- their magnitudes must be exactly equal
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.
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.
You must find the x and y components of each vector. Then you add up the like x components and the like y components. Using your total x component and total y component you may then apply the pythagorean theorem.
If their sum (resultant) is 0, then the magnitude of the resultant must be 0.
Yes, two vectors of different magnitudes can be combined to give a zero resultant if they are equal in magnitude but opposite in direction. For three vectors to give a zero resultant, they must form a closed triangle or meet at a common point where the sum of the vectors equals zero.
A triangle...
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.
In order for two vectors to add up to zero:-- their directions must be exactly opposite-- their magnitudes must be exactly equal
Not necessarily. Suppose you have three vectors (ax + by + cz), (gx + hy +iz) and (mx + ny + oz) then as long as a+g+m = b+h+n = c+i+o = 0 the resultant is zero.
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.
Yes, two vectors with different magnitudes can be combined to give a zero resultant if they are in opposite directions. However, it is not possible for three vectors with different magnitudes to give a zero resultant because they must have specific magnitudes and directions to cancel each other out completely.
The minimum number of vectors with unequal magnitudes whose vector sum can be zero is two. These vectors must have magnitudes and directions that cancel out when added together to result in a zero vector sum.
The parallelogram law of vectors states that if two vectors are represented by the sides of a parallelogram, then the diagonal of the parallelogram passing through the point of intersection of the two vectors represents the resultant vector. This means that the sum of the two vectors is equivalent to the diagonal vector.
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.
You must find the x and y components of each vector. Then you add up the like x components and the like y components. Using your total x component and total y component you may then apply the pythagorean theorem.