A vector is a two part quantity. A vector includes both a magnitude (often a distance or a force) and a direction that the magnitude is in. Most of the population deals with scalar quantites, such as 10 miles or 5 pounds. But if you were to say 10 miles northwest, you would be giving a vector.
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Vector Algebra and Vector Calculus are used widely in science, especially Physics and engineering.The physical world involves four dimensions, one scalar dimension and three vector dimensions. From this you can say that 3/4 of the world involve vectors.
Yes, a vector can be represented in terms of a unit vector which is in the same direction as the vector. it will be the unit vector in the direction of the vector times the magnitude of the vector.
The zero vector is both parallel and perpendicular to any other vector. V.0 = 0 means zero vector is perpendicular to V and Vx0 = 0 means zero vector is parallel to V.
Resultant vector or effective vector
Vector spaces can be formed of vector subspaces.