irycio said:Right side is a determinant of this matrix. It's not so hard to prove, you could in example use Levi-Civita symbol to write your cross product, it goes in 3 steps afterwards.
A dot product between cross products is a mathematical operation used to find the scalar value of two cross products. It is also known as a triple scalar product.
The dot product between cross products is calculated by taking the dot product of one of the cross products with the other cross product. This can be represented as (a x b) · (c x d), where a and b are vectors in the first cross product and c and d are vectors in the second cross product.
The dot product between cross products is significant in vector algebra and physics, as it can be used to find the angle between two vectors or the area of a parallelogram formed by the vectors.
Yes, a dot product between cross products can be negative. The sign of the dot product depends on the angle between the two cross products. If the angle is greater than 90 degrees, the dot product will be negative. If the angle is less than 90 degrees, the dot product will be positive.
The dot product between cross products has many applications in physics, engineering, and computer graphics. It is used to calculate torque, work, and power in physics. In engineering, it is used to find the moment of inertia and angular momentum. In computer graphics, it is used to determine the orientation of objects in 3D space.