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Introduction to vectors. A vector is a quantity that has both a magnitude (or size) and a direction. Both of these properties must be given in order to specify a vector completely. In this unit we describe how to write down vectors, how to add and subtract them, and how to use them in geometry.
Vector addition is sometimes referred to as the triangle law. THE PARALLELOGRAM LAW FOR VECTOR ADDITION. Another way to illustrate vector addition is to think of the resultant vector u + v as the diagonal of a parallelogram. We can complete a parallelogram by drawing copies of vectors u and v on opposite sides of each other.
Triangle Law for finding the resultant of two vectors: If 2 vectors are drawn head to tail, the vector from the tail of the first to the head of the second is the resultant.
Three numbers are needed to represent the magnitude and direction of a vector quantity in a three dimensional space. These quantities are called vector quantities. Vector quantities also satisfy two distinct operations, vector addition and multiplication of a vector by a scalar.
Vectors in R3. Introduce a coordinate system in 3-dimensional space in the usual way. First choose a point O called the origin, then choose three mutually perpendicular lines through O, called the x, y, and z axes, and establish. a number scale on each axis with zero at the origin.
Definition of vectors. In physics, some quantities (e.g. distances, volumes, temperatures, or masses) are completely charac-terized by their magnitudes, expressed with respect to a chosen unit by real numbers. These quantities are called scalars. Some others.
Mechanics: Scalars and Vectors • Scalar –Only magnitude is associated with it •e.g., time, volume, density, speed, energy, mass etc. • Vector –Possess direction as well as magnitude –Parallelogram law of addition (and the triangle law) –e.g., displacement, velocity, acceleration etc. • Tensor –e.g., stress (3 3 components)
