Question

why vectors are important in physics?

Answer 1

They are important because vector quantities give you information about both magnitude and direction. For example, speed (a scalar) only gives magnitude, but velocity (a vector) gives magnitude and direction. In some situations vectors need to be used because of the directions involved.

Answer 2

what would be the problems if there is no vector?

Answer 3

Sometimes you need to know the directions things are acting. For example, in Newton's second law, you need to know the unbalanced force acting on an object to determine its acceleration. To find the unbalanced force you need to add al of the vectors acting. You have to take directions into account to do this.