vector operations

Английский Язык - Английский Язык

Определение vector operations в Английский Язык Английский Язык словарь: Extension of the laws of elementary algebra to vectors. They include addition, subtraction, and three types of multiplication. The sum of two vectors is a third vector, represented as the diagonal of the parallelogram constructed with the two original vectors as sides. When a vector is multiplied by a positive scalar (i.e., number), its magnitude is multiplied by the scalar and its direction remains unchanged (if the scalar is negative, the direction is reversed). The multiplication of a vector a by another vector b leads to the dot product, written a b, and the cross product, written a b. The dot product, also called the scalar product, is a scalar real number equal to the product of the lengths of vectors a (a) and b (b) and the cosine of the angle () between them: a b = a b cos . This equals zero if the two vectors are perpendicular (see orthogonality). The cross product, also called the vector product, is a third vector (c), perpendicular to the plane of the original vectors. The magnitude of c is equal to the product of the lengths of vectors a and b and the sine of the angle () between them: c = a b sin . The associative law and commutative law hold for vector addition and the dot product. The cross product is associative but not commutative

vector operations