No. Let B = ai + bj + ck. When you take the cross product, each term must give a k-component or 0. We know that c must equal 0, since i X k = -j. But what about a?krot said:its only in j direction
it can't have a component of other vector
because in order to transform i to k
we need pure j
No you didn't. What's i X i?krot said:i showed purely by math that the result is pure -j vector
A cross product is a mathematical operation that takes two vectors as inputs and produces a third vector as the result. It is also known as the vector product or outer product.
The cross product is calculated using the determinant of a 3x3 matrix. The resulting vector is perpendicular to both of the input vectors and its direction is determined by the right-hand rule.
The cross product is used to find a vector that is perpendicular to two given vectors. It is also useful in calculating torque, determining the direction of a magnetic field, and in 3D graphics and physics simulations.
No, the cross product is only defined for three-dimensional vectors. For vectors in higher dimensions, the cross product does not make sense and is not defined.
The cross product results in a vector, while the dot product results in a scalar. Additionally, the cross product is only defined for three-dimensional vectors, while the dot product can be calculated for vectors in any dimension.