#400#ML_Engineer_Basic#410#Mathematics#410.00#Linear_Algebra#410.00 b#Vector_Operation

Addition and subtraction[edit]

The addition may be represented graphically by placing the tail of the arrow b at the head of the arrow a, and then drawing an arrow from the tail of a to the head of b. The new arrow drawn represents the vector a + b, as

Subtraction of two vectors can be geometrically illustrated as follows: to subtract b from a, place the tails of a and b at the same point, and then draw an arrow from the head of b to the head of a. This new arrow represents the vector (-b) + a, with (-b) being the opposite of b, see drawing. And (-b) + a = a - b.

Vector multiplication: Dot product

The dot product of two vectors a and b (sometimes called the inner product, or, since its result is a scalar, the scalar product) is denoted by a . b, and is defined as:

The dot product can also be defined as the sum of the products of the components of each vector as

Vector multiplication: Cross product

The cross product (also called the vector product or outer product) is only meaningful in three or seven dimensions. The cross product differs from the dot product primarily in that the result of the cross product of two vectors is a vector. The cross product, denoted a x b, is a vector perpendicular to both a and b and is defined as