VECTOR, in mathematics, the same as RADIUS VECTOR (q. v.). Also a directive quantity, as a straight line, a force, or a velocity. The simplest manner in which to represent such a quantity, which in volves both direction and magnitude, is by means of a straight line in space. Then the vector may be regarded as a stepping from one extremity of the line to the other. Vectors are said to be equal when their direction is the same and their magnitudes equal.
VEDA (from vid, "to know," hence "knowledge, [sacred] science"), the name of a body of religious writings which the Hindus believe to be divinely inspired. This body primarily consists of four collections (samhitd) of hymns, detached verses, and sacrificial formulas —viz., the Rig Veda, or Veda of or hymns; the Sama Veda, or Veda of chants or tunes; the Yajur Veda, or Veda of prayers; and the Atharva Veda, or Veda of the Atharvans—to each of which are attached certain theological prose works called Brahmana, and in tended chiefly to elucidate the meaning and application of the sacred texts, especially from a sacrificial point of view. The first three Vedas are often referred to as the "trayi vidyfi," or three fold science; and they alone must orig inally have formed the sacred canon, while the fourth Veda, which is less archaic in language, was not recognized till a later period. The Sahmitas of the Sfima Veda and Yajur Veda are of a purely sacrificial and professional char acter, being intended to serve as text books for two of the four chief classes of priests—viz., the chanters (Udgfitar) and the offering. priests (Adhvarvu) re spectirely; and the verses contained in them are to a large extent taken from the Riksamhita, though not unfrequently with considerable textual variations. The Riksamhita, on the other hand, though likewise assigned to a special class of priests—viz., the invokers (or sacrificers, Hotar), is not a sacrificial text-book in the same narrow sense of the word; but it has rather to be looked on as a collection of all the sacred poetry which was within reach of the collectors, and seemed to them worthy of being preserved for devotional purposes.
The Rig Veda samhita has come down to us in a single recension, that of the S'akala school. It consists of 1,028 hymns composed in various meters, and arranged in 10 books or mandalas. Book i. is mainly made up of 16 collections of hymns ascribed to as many poets be longing to different families. Books ii. vii., on the other hand, are attributed each to a special family of Rishis or seers—viz., the Gritsamadas, Kus'ikas (or Vis'vamitras), Vamadevyas, Aatris, Bharadvajas, and Vasishthas respective ly—whence they are usually called the family books.
The Sama Veda-samhita consists of two parts (or archika), the first of which contains the (585) verses to which the several saman tunes are usually ,sung, while the second gives the text of the made-up chants in the order in which they are required in the sacri ficial ritual. The tunes themselves, on
the other hand, are given in four special tune-books, called Gana, attached to the Samhita. The latter, consisting as it does mainly of detached verses taken from the Riksamhita, has only a tech nical interest. The mode of chanting somewhat resembled the Gregorian or Plain chant. The Brahmanas of this Veda have a special character of their own, inasmuch as they are not different versions, or editions, of the same tradi tional exegetic and legendary matter, but altogether distinct treatises, dealing chiefly with chants.
The Yajur Veda offers the spectacle of a complete schism, its teachers and followers dividing themselves into an older and you,nger branch, or the Black and the White Yajur Veda, so called from the form in which their canonical books were handed down. For while the scriptures of the older branch presented a somewhat confused appearance, caused by the constant, intermingling of the sacrificial formulas (yajus) and the exe getic portions (brahmana), the young er school adopted the practice of the followers of the Rik by dividing their scriptures into a regular Samhita, or collection of sacrificial formulas and a Brahmana.
The Atharva Veda-samhita is a collec tion of hymns and spells which, in im portance and interest, ranks next to the Riksamhita. The two collections pre sent two different aspects of the re ligious belief of the ancient Hindus. While the Rik reflects a simple belief in divine powers who are, on the whole, well disposed toward the Aryan man, and whose favor the worshiper is con fident of gaining by his song, the Athar van, on the other hand, reveals a super stitious dread of a host of malevolent powers, the effects of whose ill will man seeks to avert by means of incanta tions and magic practices. A recension discovered in Kashmir not only differs from it considerably in its arrangement, but also contains some new matter, amounting to about one-sixth of the whole. The Brahmana of this Veda, the Gopatha (or cow-path)-brahmana, con taining cosmogonic speculations and ex planations of certain sacrificial rites, is probably a comparatively modern work; while of the two ceremonial sutras, the Vaitana (or s'rauta)-sutra and the Kaus'ika-sutra, a manual of domestic rites, the latter is by far the more in teresting. The Atharva Veda has also usually assigned to it a large number of Upanishads, amounting to consider ably over 100. They are evidently of various ages, many of them coming down to very recent times.