[justify]In the worksheet there is a set of questions willing to explore about the direction angles of the vector to the sign (or nullity) of their respective component, examples of questions asked in the worksheet are: [br]i) If the [math]x[/math] component of the vector is positive, what is the range of values for the angle between the vector and the [math]x[/math] axis? (similar questions for [math]y[/math] and [math]z[/math] components).[br]ii) If the [math]y[/math] component of the vector is negative, what is the range of values for the angle between the vector and the [math]y[/math] axis? (similar questions for [math]x[/math] and [math]z[/math] components).[br]iii) If the [math]z[/math] component is zero, what is the angle between the vector and the [math]z[/math] axis? (similar questions for [math]x[/math] and [math]y[/math] components).[br]iv) if the magnitude of the vector is equal to the [math]y[/math] component, what is the angle between the vector and the [math]y[/math] axis? (similar questions for [math]x[/math] and [math]z[/math] components, as well as considering a component equal to the negative of the magnitude).[br] [br]To help students answering these questions, each of the components are gradually changed from positive to negative, keeping the view of the angle to observe and hiding the other angles to avoid confusion, the values of the angle can be read from the algebra view, but the range is easily seen from the 3D view without any particular orientation of the image, it only has to be clear which one is the angle to observe and the respective component along with the vector.[/justify]