1 Scalars and Vectors is a number which expremay or may not have units associated with themExamples mass volume energy money s both magnitude and direction The magnitude of a vector is a scala ID: 162906
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1 Scalars and Vectors Scalars and Vectors is a number which expremay or may not have units associated with them.Examples: mass, volume, energy, money s both magnitude and direction. The magnitude of a vector is a scalar.Examples: Displacement, velocity, acceleration, electric field 2 Vectors are denoted as a symbol with an arrow over the top:Vectors can be written as a magnitude and direction: deg30@CN7.15oE Vectors are represented by an arroThe length of the vector represents the magnitude of the vector.WARNING!!! The length of the arrow does not necessarily sm3.2A 3 Vector Addition A B Adding Vectors Graphically. Arrange the to tail fashion. A The resultant is drawn from the tail of the first to the head of the last This works for any number of B C D DCBAR 4 Vector Addition Vector Subtraction A B Subtracting Vectors Graphically. A Flip one vector.Then proceed to add the vectors The resultant is drawn from the tail of the first to the head of the last ABAC B 5 Example:from the horizontal. Find its components. rrxcos jrrysino30@m0.5r irirxxm3.430cosm0.5o jrjryym5.230sinm0.5o Any vector can be broken down into components along You can add two vectors by adding the components of the vector along each direction. Note that you can only add components which lie along the same direction. jsmismBAjsmismBjsmismA7.77.42.55.15.22.3 m4.12BA Never add the x-component and the y-component 6 Unit Vectors Unit vectors have a magnitude of 1. y A displacement of 5 m in The magnitude is 5m.The direction is the î-direction. Finding the Magnitude and Direction r xr yr 22yxrrr xyrrtan xyrr1tan Pythagorean Theorem 7 Vector Multiplication I: The Dot ProductThe result of a dot product of two vectors is a scalarcosABBA 111 k k jjii000 k ikjji Vector Multiplication I: The Dot Product N232kjiF m643kjis sF mN)3(2 mN)4(3 mN)6)(2( mN6sF 8 Vector Multiplication II: The Cross Product sinABBA 000 k k jjiijikikjkjiThe result of a cross product of two vectors is a new vector C Vector Multiplication II: The Cross Product BqvBvqBvq C BAABC AC BC 9 Vector Multiplication II: The Cross Product N232kjiF m643kjir Fr kijiiim6N2m4N2m3N2 kkjkikm6N2m4N2m3N2 mN17626kji Vector Multiplication II: The Cross Product N232kjiF m643kjir Fr mN17626kji i6324 j23262364jk2236ki3243ij k4233 10 Vector Multiplication II: Right Hand Rule Thumb points in the WARNING: Make sure you