Depends on the situation.
Vector A x Vector B= 0 when the sine of the angle between them is 0
Vector A . Vector B= 0 when the cosine of the angle between them is 0
Vector A + Vector B= 0 when Vectors A and B have equal magnitude but opposite direction.
With three vectors spaced 120 degrees apart and with identical magnitudes the vector sum will be 0.
The component vector sum is zero and the all components cancel out.:)
The subtraction of two vectors equals zero when the two vectors are identical in both magnitude and direction. Mathematically, if vector A minus vector B equals the zero vector (A - B = 0), then A must be equal to B. This implies that they point in the same direction and have the same length.
I think you meant to ask for finding a perpendicular vector, rather than parallel. If that is the case, the cross product of two non-parallel vectors will produce a vector which is perpendicular to both of them, unless they are parallel, which the cross product = 0. (a zero vector)
The dot product of two perpendicular vectors is 0. a⋅b = |ab|cos θ where: |a| = length of vector a |b| = length of vector b θ = the angle between the vectors. If the vectors are perpendicular, θ = π/2 radians → cos θ = cos(π/2) = 0 → a⋅b = |a| × |b| × 0 = 0 ----------------------------------------------------------------------------- The dot product can also be calculated for vectors of n dimensions as the sum of the products of the corresponding elements: a = (a1, a2, ..., an) b = (b1, b2, ..., bn) a⋅b = Σ ar × br for r = 1, 2 , ..., n With perpendicular vectors this sum is zero,
With three vectors spaced 120 degrees apart and with identical magnitudes the vector sum will be 0.
Two vectors; V1 + V2=0 where V1= -V2, two opposite vectors.
The component vector sum is zero and the all components cancel out.:)
If A + B = 0, this means that vector A is equal in magnitude but opposite in direction to vector B. In other words, the two vectors are anti-parallel to each other. This relationship indicates that the components of the two vectors cancel each other out when added together, resulting in a net vector of zero.
-- A singe vector with a magnitude of zero produces a zero resultant.-- Two vectors with equal magnitudes and opposite directions produce a zero resultant.
The subtraction of two vectors equals zero when the two vectors are identical in both magnitude and direction. Mathematically, if vector A minus vector B equals the zero vector (A - B = 0), then A must be equal to B. This implies that they point in the same direction and have the same length.
I think you meant to ask for finding a perpendicular vector, rather than parallel. If that is the case, the cross product of two non-parallel vectors will produce a vector which is perpendicular to both of them, unless they are parallel, which the cross product = 0. (a zero vector)
The vectors A and B seem to be two-dimensional with components in the x and y directions. The components of vector A are A_x and A_y, while the components of vector B are B_x and B_y. The 0 value suggests that one or both of the vectors have a component equal to zero.
The dot product of two perpendicular vectors is 0. a⋅b = |ab|cos θ where: |a| = length of vector a |b| = length of vector b θ = the angle between the vectors. If the vectors are perpendicular, θ = π/2 radians → cos θ = cos(π/2) = 0 → a⋅b = |a| × |b| × 0 = 0 ----------------------------------------------------------------------------- The dot product can also be calculated for vectors of n dimensions as the sum of the products of the corresponding elements: a = (a1, a2, ..., an) b = (b1, b2, ..., bn) a⋅b = Σ ar × br for r = 1, 2 , ..., n With perpendicular vectors this sum is zero,
The magnitude of a vector is 0 if the magnitude is given to be 0.The magnitude of the resultant of several vectors in n-dimensional space is 0 if and only if the components of the vectors sum to 0 in each of a sewt of n orthogonal directions.
For two vectors A and B, the scalar product is A.B= -ABcos(AB), the minus sign indicates the vectors are in the same direction when angle (AB)=0; the vector product is ABsin(AB). Vectors have the rule: i^2= j^2=k^2 = ijk= -1.
Vectors. A scalar times a vectro is a vector. A vector times a vector is a scalr if the vectros are parallel v1.v2 = scalar. A vector times a vector is a vector if the vectors are perpendicular. Other wise a vectro times a vector is both a scalr and a vector, v1v2 = -v1.v2 + v1xv2 = -v1v2cos(x) + vqv2sin(x). If cos(x) =0 then perpendicular if sin(x)=0 then parallel. In general the product of two vectors is a quaternion the sum of a scalar and a vector. The Universe is composed of quaternions. Science and Physics has failed to appreciate that the numbes of the universe are quaternions, the sum of a scaltr and a vector. Hamilton invented quaternions in 1843.