Practice the dot product

Compute the dot product of the following pairs of vectors:




    A  =  (  6 , 0 )             B  =  (  3 ,     )


    C  =  ( -4 , 2 )             D  =  (  2 , 4   )


    E  =  ( -5, -5 )             F  =  (  1 ,     )


    G  =  (  3,  4 )             H  =  5 units at -30 degrees

 
    I  =  6 m at 120 degrees     J  =  3 m at 70 degrees


    K  =    m at -45 degrees     L  =  5 m at 10 degrees

What is the angle between each of these pairs of vectors?



    M  =  (  0 ,  6 )            N  =  (  0 , 10 )


    P  =  (  0 ,  6 )            Q  =  ( 10 ,  0 )


    R  =  (  2 ,    )            S  =  ( -3 ,  7 )

Joe (mass m = 38 kg) slides down a hill on his sled. "Wheeeee!" exclaims Joe, as he shoots 20 meters down the slope, which has an angle of 35 degrees below the horizontal.

What is the force of gravity on Joe? Express as a vector.
What is Joe's displacement? Express as a vector.
What is the dot product of Joe's displacement and the force of gravity on Joe? Don't forget the units.