What is the direction of g? What is the direction of w?

Answer

The direction of g (gravitational field strength or acceleration due to gravity) is always directed towards the center of the mass creating the gravitational field; in the context of Earth, this is vertically downward. The direction of w (weight) is also vertically downward, towards the center of the Earth, as weight is the gravitational force acting on an object. Since weight is defined by the product of mass (a scalar) and g (a vector), the direction of the weight vector must be parallel to the direction of the gravitational field intensity vector.