Vector
in mathematics, the same as and magnitude, is RADIUS VECTOR (q. v.). Also a directive volves both direction and quantity, as a straight line, a force, or a velocity. The simplest manner in which to represent such a quantity, which inby means of a straight line in space. stepping from one extremity of the line Then the vector may be regarded as a when their direction is the same and to the other. Vectors are said to be equal their magnitudes equal.
VEDA (from vid, "to know," hence name of a body of religious writings inspired. This body primarily consists "knowledge, [sacred] science"), the detached verses, and sacrificial formulas name of a body of religious writings or hymns; the Sâma Veda, or Veda of of four collections (samhita) of hymns, - viz., the Rig Veda, or Veda of praises or Veda of the Atharvans to each of which are attached certain theological chants or tunes; the Yajur Veda, or Veda of prayers; and the Atharva Veda, prose works called Brahmana, and inespecially from a sacrificial point of which are attached certain theological prose works called Brâhmana, and inand application of the sacred texts, view. The first three Vedas are often referred to as the "trayî vidya," or threearchaic in language, was not recognized fold science; and they alone must originally have formed the sacred canon, while the fourth Veda, which is less till a later period. The Sahmitâs of the Sâma Veda and Yajur Veda are of a purely sacrificial and professional character, being intended to serve as textbooks for two of the four chief classes of priests-viz., the chanters (Udgâtar) and the offering priests (Adhvaryu) re- Vol. X VEDA spectively; and the verses contained in them are to a large extent taken from the Riksamhitâ, 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 samhitâ has come down to us in a single recension, that of the S'âkala 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 belonging 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'vâmitras), Vâmadevyas, Aatris, Bharadvâjas, and Vasishthas respectively-whence they are usually called the family books. of The Sâma Veda-samhitâ consists of two parts (or ârchika), the first of which contains the (585) verses to which the several sâman 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 sacrificial ritual. The tunes themselves, on the other hand, are given in four special tune-books, called Gâna, attached to the Samhitâ. The latter, consisting as it does mainly of detached verses taken from the Riksamhita, has only a technical interest. The mode of chanting somewhat resembled the Gregorian or Plain chant. The Brâhmanas of this Veda have a special character of their own, inasmuch as they they are not different versions, or editions, of the same traditional 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 younger 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 exegetic portions (brâhmana), the younger school adopted the practice of the followers of the Rik by dividing their scriptures into a regular Samhita, or VEDANTA collection of sacrificial formulas and a Brâhmana.
The Atharva Veda-samhitâ is a collection of hymns and spells which, in importance and interest, ranks next to the Riksamhita. The two collections present two different aspects of the religious 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 confident of gaining by his song, the Atharvan, on the other hand, reveals a superstitious dread of a host of malevolent powers, the effects of whose ill will man seeks to avert by means of incantations 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 Brâhmana of this Veda, the Gopatha (or cow-path)-brâhmana, containing cosmogonic speculations and explanations of certain sacrificial rites, is probably a comparatively modern work; while of the two ceremonial sûtras, the Vaitâna (or s'rauta)-sûtra and the Kausika-sûtra, a manual of domestic rites, the latter is by far the more interesting. The Atharva Veda has also usually assigned to it a large number of Upanishads, amounting to considerably over 100. They are evidently of various ages, many of them coming down to very recent times.