VECTOR OPERATIONS


Meaning of VECTOR OPERATIONS in English

Extension of the laws of elementary algebra to vector s.

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 22C5; b , and the cross product, written a 00D7; b . The dot product, also called the scalar product, is a scalar real number equal to the product of the lengths of vectors a ( 007C; a 007C; ) and b ( 007C; b 007C; ) and the cosine of the angle ( 03B8; ) between them: a 22C5; b = 007C; a 007C; 007C; b 007C; cos 03B8; . 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 ( 03B8; ) between them: 007C; c 007C; = 007C; a 007C; 007C; b 007C; sin 03B8; . The associative law and commutative law hold for vector addition and the dot product. The cross product is associative but not commutative.

Britannica Concise Encyclopedia.      Краткая энциклопедия Британика.