Vector has both magnitude and direction. What is this direction I'm talking about? Now is the moment to clear your doubt. Take force as an example,
Student A uses 5N to push towards >> direction
Student B uses 6N to push towards >> direction
So the total force would be 11N towards >> direction.
It can also be in this case...
Student A uses 7N to push towards >> direction
Student B uses 4N to push towards << direction
This means that both forces are acting on each other. But student A exerts more force than student B so the force would be 3N acting towards >> direction. Easy isn't it?
The sum of two vector is known as resultant.
Vector can be calculated using a parallelogram method.
Sorry I have very limited source so I couldn't show it to you..
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