The scalar multiplication of two vectors is known as the scalar or dot product. As the name indicates, the scalar product of two vectors results in a number, that is, a scalar quantity. Scalar products are used to define work and energy relations. For example, the work that a force (a vector) performs on an object while causing its displacement (a vector) is defined as a scalar product of the force vector with the displacement vector.
The scalar product of two vectors is obtained by multiplying...

Vector multiplication of two vectors yields a vector product, with the magnitude equal to the product of the individual vectors multiplied by the sine of the angle between both the vectors and the direction perpendicular to both the individual vectors. As there are always two directions perpendicular to a given plane, one on each side, the direction of the vector product is governed by the right-hand thumb rule.
Consider the cross product of two vectors. Imagine rotating the first vector about...

Rate-programmed drug delivery systems release drugs in a controlled manner to maintain therapeutic levels. Three main designs include reservoir, matrix, and hybrid systems.Reservoir systems consist of a drug core enclosed within a membrane that controls drug release. In non-swelling reservoir systems, polymers like ethyl cellulose or polymethacrylates are used. These do not hydrate in aqueous media and control release through membrane thickness, porosity, or insolubility. This type includes...

Rate-programmed drug delivery systems (DDS) are designed to release drugs at specific, controlled rates to maintain consistent therapeutic levels. These systems are categorized based on their release mechanisms, including dissolution-controlled DDS, diffusion-controlled DDS, and combined dissolution-diffusion-controlled DDS.In dissolution-controlled DDS, the release rate depends on the slow dissolution of the drug itself or the surrounding matrix. Drugs with inherently slow dissolution rates,...