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Chapter 2,[object Object],Vectors,[object Object]
In this chapter, we will discuss the following:,[object Object],the difference between scalar and vector quantities;,[object Object],representing vectors graphically;,[object Object],resultant and equilibrant vectors; and,,[object Object],finding resultant vector,[object Object]
Vectors and Scalars,[object Object]
Vectors and Scalars,[object Object]
Representing Vectors,[object Object],A vector is represented by an arrow.,[object Object],The length of the arrow is proportional to the magnitude of the vector.,[object Object],The tail indicates the starting point.,[object Object],The orientation of the arrowhead indicates the direction.,[object Object],Vectors maybe denoted using a boldface type (i.e. A denotes vector A).,[object Object]
Representing Vectors,[object Object]
Vector Addition,[object Object],Vector addition is different from the usual addition in arithmetic.,[object Object],The magnitude and direction should be taken into consideration.,[object Object],Only vectors of the same kind can be added or combined.	,[object Object]
Properties of Vector Addition,[object Object],Commutative  : The order of addition does not matter.,[object Object],A + B = B + A,[object Object],Associative :  The grouping does not matter in adding 2 or more vectors.,[object Object],(A + B) + C = A + (B + C),[object Object]
Resultant and Equilibrant,[object Object]
Finding Resultant Vector,[object Object],Graphical Method or Polygon Method,[object Object],Use a ruler and a protractor.,[object Object],Analytical Method,[object Object],Requires some knowledge in trigonometry.,[object Object]
Graphical / Polygon Method,[object Object],Draw 1st vector using a convenient scale.,[object Object],From the terminal point (head) of the 1st vector, draw 2nd vector; from the terminal point (head) of the 2nd vector, draw 3rd vector; and so on, until the last vector.,[object Object],Draw the resultant vector (R) from the initial point (tail) of the 1st vector to the terminal point (head) of the last vector.,[object Object],Measure the resultant vector R using a ruler and a protractor to find its magnitude and direction. ,[object Object]
Analytical / Component Method,[object Object]
Analytical / Component Method,[object Object]
Finding Resultant Vector,[object Object],Answer: 950m East,[object Object]
Finding Resultant Vector,[object Object],Answer: 300m West,[object Object]
Finding Resultant Vector,[object Object],Answers : ,[object Object],a. 7km,[object Object],b. 5km, 53.13o  N of E,[object Object]
Finding Resultant Vector,[object Object],Answer : 6.17cm, 45.85o  N of E,[object Object]
Solution for Example 4,[object Object],0o,[object Object],0,[object Object],2,[object Object],40o,[object Object],1.93,[object Object],2.30,[object Object],90o,[object Object],0,[object Object],2.5,[object Object],4.30,[object Object],4.43,[object Object],Direction:,[object Object],Magnitude:,[object Object]
Finding Resultant Vector,[object Object],Answer : 15.80m, 29.71oN of W,[object Object]
Solution for Example 5,[object Object],50o,[object Object],3.83,[object Object],3.21,[object Object],150o,[object Object],4,[object Object],-6.93,[object Object],180o,[object Object],-10,[object Object],0,[object Object],-13.72,[object Object],7.83,[object Object],Direction:,[object Object],Magnitude:,[object Object],R = 15.8m,[object Object],θ = 150.290,[object Object],29.71o N of W,[object Object]
TRY THIS!!!,[object Object]

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