what is cross product or vector product plz explain it in detail.....
The cross product, also known as the vector product, is an operation between two vectors that yields a new vector orthogonal (perpendicular) to both of the original vectors. It is denoted by the symbol "×".
To understand the cross product, let's consider two vectors, A and B, in three-dimensional space. The cross product of A and B is given by:
A × B = |A| |B| sinθ n
where |A| and |B| are the magnitudes of the vectors A and B, θ is the angle between them, and n is the unit vector perpendicular to the plane formed by A and B, following the right-hand rule.
To calculate the cross product, follow these steps:
1. Calculate the magnitude of the cross product: |A × B| = |A| |B| sinθ.
The magnitude of the cross product is equal to the product of the magnitudes of A and B, multiplied by the sine of the angle between them.
2. Determine the direction of the cross product using the right-hand rule.
Hold your right hand with your fingers pointing in the direction of the first vector (A) and curl them towards the second vector (B). Your thumb will point in the direction of the resulting cross product vector.
If you reverse the order of the vectors (B × A), the direction of the resulting cross product will be opposite.
3. Normalize the cross product vector.
To normalize the cross product vector, divide it by its magnitude: n = (A × B) / |A × B|.
In addition to finding the magnitude and direction of the resultant vector, the cross product has various applications in physics, such as calculating torque, angular momentum, and electromagnetic fields.
It's important to note that the cross product only applies to vectors in three-dimensional space and is not defined in higher-dimensional spaces.