Not at all. All that AxB=AxC says is that either A=0 (in which case any two vectors B and C satisfy AxB=AxC), or that the components of B and C normal to A are equal.cp255 said:
The cross product of two vectors is a mathematical operation that results in a third vector that is perpendicular to the two input vectors. It is also known as the vector product or outer product.
The cross product is calculated by taking the determinant of a 3x3 matrix formed by the components of the two input vectors, with the first row being the unit vectors i, j, and k, the second row being the components of the first vector, and the third row being the components of the second vector.
The cross product can be interpreted geometrically as the area of the parallelogram formed by the two input vectors, with the direction of the resulting vector being perpendicular to the plane of the parallelogram.
The cross product is related to the dot product by the identity a x b = |a||b|sinθ, where a and b are the input vectors and θ is the angle between them. This means that the cross product is zero when the two vectors are parallel, and reaches its maximum value when the two vectors are perpendicular.
The cross product has many applications in physics, engineering, and computer graphics. It is used to calculate torque, magnetic fields, and angular momentum in physics, and is also used in 3D graphics to calculate lighting and shading effects.