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INTRODUCING VECTORS. 1.1 Scalars. 1.2 Vectors. 1.3 Unit vectors. 1.4 Vector algebra. 1.5 Simple examples. 1.1 Scalars. A scalar is a quantity with magnitude but no direction, any mathematical entity that can be represented by a number. Examples: Mass, temperature, energy, charge ...
Example. Write the polar unit vectors r and θ in terms of the Cartesian unit vectors x and y . Unit Vectors. We are familiar with the unit vectors in Cartesian coordinates, where . points in the x-direction and . y-direction.
Let xˆ be a vector of unit magnitude pointing in the positive x-direction, yˆ, a vector of unit magnitude in the positive y-direction, and zˆ a vector of unit magnitude in the positive z-direction. Then xˆAx is a vector with magnitude equal to |Ax| and in the x-direction. By vector addition, A =xˆAx +yˆAy + ˆzAz. (1.5)
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.
Many of you will know a good deal already about Vector Algebra — how to add and subtract vectors, how to take scalar and vector products of vectors, and something of how to describe geometric and physical entities using vectors.
Galileo Galilee. 3.1.1 Introduction to Vectors. Certain physical quantities such as mass or the absolute temperature at some point in space only have magnitude. A single number can represent each of these quantities, with appropriate units, which are called scalar quantities.
The force acting on an object is a vector. The direction of the vector specifies the line of action of the force, and the magnitude specifies how large the force is. Other examples of vectors include position; acceleration; electric field; electric current flow; heat flow; the normal to a surface.
