- #1
| A1 A2 A3 |
A o B x C = B o C x A = C o A x B = | B1 B2 B3 |
| C1 C2 C3 |
where 'o' is the dot product and 'x' is the cross productThe vector product, also known as the cross product, is defined as a mathematical operation between two vectors in three-dimensional space. It represents the product of the magnitude of the two vectors and the sine of the angle between them.
Scalar quantities have only magnitude and no direction, while vector quantities have both magnitude and direction. Scalar quantities include time, mass, and temperature, while vector quantities include displacement, velocity, and force.
A change in vector product can affect the resulting vector in two ways: by changing the magnitude or by changing the direction. When the angle between the two vectors changes, the magnitude of the resulting vector will also change. When one of the vectors is multiplied by a scalar, the direction of the resulting vector will change.
The right-hand rule is a method used to determine the direction of the resulting vector when performing a vector product. It states that if the fingers of the right hand curl in the direction of the first vector and then curl towards the second vector, the thumb will point in the direction of the resulting vector.
Yes, vector product has many applications in various fields, including physics, engineering, and computer graphics. It is used to calculate torque, determine the direction of magnetic fields, and create 3D images. It is also used in navigation systems, robotics, and video game development.