Vector ComponentsCoordinatesOrdered SetComponent AdditionScalar MultiplicationComponent SubtractionUse of AnglesComponents to AnglesVector ComponentsVector ComponentsCoordinatesCoordinatesVectors can be described in terms of coordinates.Vectors can be described in terms of coordinates.•6.0 km east and 3.4 km south6.0 km east and 3.4 km south•1 m forward, 2 m left, 2 m up1 m forward, 2 m left, 2 m upCoordinates are associated with axes in a graph.Coordinates are associated with axes in a graph.yxx = 6.0 my = -3.4 mOrdered SetOrdered SetThe value of the vector in The value of the vector in each coordinate can be each coordinate can be grouped as a set.grouped as a set.Each element of the set Each element of the set corresponds to one corresponds to one coordinate.coordinate.The elements, called The elements, called componentscomponents, are scalars, not , are scalars, not vectors.vectors.)66.3 ,23.4(),(AAAAyx)23 ,510 ,12(),,(...vvvvvzyxComponent AdditionComponent AdditionA vector equation is actually A vector equation is actually a set of equations.a set of equations.•One equation for each One equation for each componentcomponent•Components can be added Components can be added and subtracted like the and subtracted like the vectors themselvesvectors themselves)m 4,m 5(),(m 4m 5),()m 4,m 2(),()m 0,m 3(yxyyyxxxyxyxCCCBACBACBACBBBAAAScalar MultiplicationScalar MultiplicationA vector can be multiplied by A vector can be multiplied by a scalar.a scalar.•For instance, walk twice as For instance, walk twice as far as in the hiking example.far as in the hiking example.Scalar multiplication Scalar multiplication multiplies each component multiplies each component by the same factor.by the same factor.The result is a new vector, The result is a new vector, always parallel to the original always parallel to the original vector.vector.),(yxsAsAAsT Component SubtractionComponent SubtractionMultiplying a vector by Multiplying a vector by 1 will create an antiparallel 1 will create an antiparallel vector of the same magnitude.vector of the same magnitude.Vector subtraction is equivalent to scalar Vector subtraction is equivalent to scalar multiplication and addition.multiplication and addition.yyyyyxxxxxBABACBABACBABAC)1()1()1(Use of AnglesUse of AnglesFind the components of Find the components of vector of magnitude 2.0 km vector of magnitude 2.0 km at 60at 60° up from the x-axis.° up from the x-axis.Use trigonometry to convert Use trigonometry to convert vectors into components.vectors into components.•xx = = rr cos cos •yy = = rr sin sin yxx = (2.0 km) cos(60°) = 1.0 kmy = (2.0 km) sin(60°) = 1.7 km60°Components to AnglesComponents to AnglesFind the magnitude and Find the magnitude and angle of a vector with angle of a vector with components x = -5.0 m, y = components x = -5.0 m, y = 3.3 m.3.3 m.nextyxx = -5.0 my = 3.3 m = 33o above the negative x-axisL)/(tan/tan122222xyxyyxLyxLL = 6.0
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