Question

Define dot product, inner product, cross product.

Answer 1

- A dot product is the product of the magnitude of the vectors and the cos of the angle between them.

- A cross product is the product of the magnitude of the vectors and the sine of the angle that they subtend on each other.

- An inner product is a generalization of the dot product.

Explanation:

Dot product - the sum of the products of the corresponding entries of the two sequences of numbers. Geometrically, it is the product of the Euclidean magnitudes of the two vectors and the cosine of the angle between them. These definitions are equivalent when using Cartesian coordinates.

Cross Product - The cross product is a mathematical operation which can be done between two three-dimensional vectors. It is often represented by the symbol. After performing the cross product, a new vector is formed. The cross product of two vectors is always perpendicular to both of the vectors which were "crossed".

Inner product - In a vector space, it is a way to multiply vectors together, with the result of this multiplication being a scalar.

Answer 2

Dot product. ... In Euclidean geometry, the dot product of the Cartesian coordinates of two vectors is widely used and often called "the" inner product (or rarely projection product) of Euclidean space even though it is not the only inner product that can be defined on Euclidean space; see also inner product space.

Explanation: