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in terms of the Cartesian unit vectors x and y . Unit Vectors We are familiar with the unit vectors in Cartesian coordinates, where x points in the x-direction and y points in the
OUTLINE : 1. 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 ...
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.
these units can be used to describe other physical quantities such as velocity (m/s), and acceleration (m/s2). Sometimes the string of units gets to be so long that we contract them into a new unit called a derived unit. For example, A unit of force has base units of kg m s2! newton or N where the newton (N) is a derived unit. 3.1 Physical ...
1.1.2 The vector A whose magnitude is 1.732 units makes equal angles with the coordinate axes. Find Ax,Ay, and Az. 1.1.3 Calculate the components of a unit vector that lies in the xy-plane and makes equal angles with the positive directions of the x- and y-axes. 1.1.4 The velocity of sailboat A relative to sailboat B, vrel, is defined by the ...
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.
10.3 Unit Vectors Let’s do an example of a vector cross-product using two 3-dimensional vectors: A~= 2^i ^j+ k^ and B~=^i+ 2^j + 3k^ C~= A~ B~= ^i ^j ^k 2 1 1 1 2 3 = ^i( 3 2) + ^j(1 6) + k^(4 + 1) (1) C~= A~ B~ = 5^i 5^j + 5k^ (2) We can also write this vector in a \graphical" representation C~= jC~jC^ where C^
