Quiz#2.

 Q1.      Vector A has negative x componet 5.0 units in length and a positive y component 8.0 units in length.

            (a) Write down an expression for A  in unit vector notation.

                                 A = - 5 i + 8 j

             (b) Determine the magnitude and direction of vector A.

               A =    (Ax2 +Ay2 ) =     (-5)2+82   = 9.43

                                                                                                               tan a   = Ay/Ax= 8/5;  a = 58o   ; \  q  = 122o

             (c) What vector B when added to A gives a resultant vector with no x                     component and a negative y component 4.00 units in length? (Give B in unit vector notation)

 Given                          B + A  = - 4 j,

            then                              B = - 4 j A = - 4 j ( - 5 i + 8 j )

                         Hence,             B = 5 i  - 12 j

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Q2.      Given two vectors P = 4.0 i + 5 j and Q = 6.0 i - 8.0 j,

 (i)                  find A B, and

                         P Q = (4.0 i + 5 j ) (6.0 i - 8.0 j )

                                  = (4x6)(ii) + (4x(-8))(ij) + (5x6)(ji) +(5x(-8))(jj)    

                                  = 24 + 0 + 0 - 40                                  

                                  = - 16    

 (ii)            find the angle between the two vectors.

                        P Q = P Q cos q

                        \ cos q  = P Q / ( A B )

                                      =  -16 / ( 42+52 ) ( 62+82   )  = - 0.250

                                     q  = 105o.