Why do scientists track the energy in a system?

The supply of energy and of each needed chemical element restricts a system operation -- for example , without inputs of energy ( sunlight ) and matter ( carbon dioxide and water ) , a plant cannot grow. Hence , it is very informative to track the transfers of matter and energy within , into , or out of any system under study.

Hope it helps

potential energy is directly proportional to height.

more height = more potential energy.

greatest increase in height = greatest increase in potential energy

where are the points with the greatest increase in height ?

has to be c-e or d-e .

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west