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1.1 Unit Vectors 1. Find the unit vector in the direction w⃗= (5,2). Solution: A unit vector in physics is defined as a dimensionless vector whose magnitude is exactly 1. A unit vector that points in the direction of A⃗is determined by formula Aˆ = A⃗ |A⃗| Where |A|is the magnitude of the vector A⃗with the following formula |A⃗|= q ...
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 ...
Unit vectors are vectors of length 1 that point in the desired direction. The best known unit vectors are i and j which point in the positive x and y directions respectively. You generate unit vectors by first find a vector that points the right way and then dividing by the
Vector Practice. 1. Draw the components of each vector in the following diagrams. Then calculate the length of each component. 5. If I walk 20 miles North, then 15 miles East, then 10 miles at 35° South of East, What distance have I traveled? What is my displacement? If I travel the entire distance in 4 hours, then what is my average velocity?
Figure 3: Figure P1.80 from University Physics 14th edition 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) 10
Vectors enter physics in two distinct forms. (1) Vector A may represent a single force acting at a single point. The force of gravity acting at the center of gravity illustrates this form. (2) Vector A may be defined over some extended region; that is, A and its compo-nents may be functions of position: Ax = Ax(x,y,z),and so on. Examples of ...
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 ...
