Why can the cross product of two vectors be calculated by the second-order determinant The cross product of vector AB and vector ad is ab × ad. the vector AB is expressed as (BX ax, by ay), and the vector ad is expressed as (DX ax, Dy ay). The two vectors can be expressed as a second-order determinant |Bx-Ax,By-Ay| |Dx-Ax,Dy-Ay| After expansion, we can get (BX ax) * (Dy ay) - (DX ax) * (by ay) ------------------------------------------------------------ I just know mechanically that it should be calculated like this, but why can the cross product of vector be calculated by two-stage determinant? It's difficult to understand. What's the connection between the two

Why can the cross product of two vectors be calculated by the second-order determinant The cross product of vector AB and vector ad is ab × ad. the vector AB is expressed as (BX ax, by ay), and the vector ad is expressed as (DX ax, Dy ay). The two vectors can be expressed as a second-order determinant |Bx-Ax,By-Ay| |Dx-Ax,Dy-Ay| After expansion, we can get (BX ax) * (Dy ay) - (DX ax) * (by ay) ------------------------------------------------------------ I just know mechanically that it should be calculated like this, but why can the cross product of vector be calculated by two-stage determinant? It's difficult to understand. What's the connection between the two

There is no cross product operation for vectors in two-dimensional plane
Your second-order determinant is not a cross product operation, because it only makes sense in three-dimensional space
As for you insist on defining this kind of determinant operation, its value is actually related to the angle between AB and AD
Let a = (A1, A2), B = (B1, B2), and the included angle be θ,
There is a formula: Tan θ = (A1 * b2-a2 * B1) / (A1 * B1 + A2 * B2)

Is the vector product a matrix or a determinant

Determinant, matrix can not be transformed into formula

What is the physical meaning of dot product and cross product of vector

What is the physical meaning of dot product and cross product of vector
A: given vectors a and B, their dot product A & # 8226; b = ︱ a ︱ B ︱ cos θ, where θ is the angle between a and B,
The point product is used to express the work done by the force. When the angle between the force F and the displacement s of the particle is θ, the work done by the force F is w = ︱ f ︱ s ︱ cos θ
=F &; s, work is quantity, so dot product is also called quantity product, undirected product, etc
The cross product of two vectors a × B = ︱ a ︱ B ︱ sin θ, where θ is the angle between a and B. in mechanics, a pair of forces is represented by the cross product
The moment of a fixed point m = R × F, when f is not perpendicular to the radial R, there is an angle θ between them, then M = R f sin θ, force
The moment M is a vector, so the cross product is also called vector product, directed product, etc.; C = a × B, the direction of C is defined by the right-hand rule: set three vectors
A. B, C attached to the same starting point, the right thumb along the direction of a, index finger along the direction of B, then the middle finger is pointing
C direction